SCERT Maharashtra solutions for Algebra (Mathematics 1) [English] 10 Standard SSC chapter 2 - Quadratic Equations [Latest edition]

Choose the correct alternative answer for the following sub questions and write the correct alphabet.

Which of the following is a quadratic equation?

Choose the correct alternative answer for the following sub questions and write the correct alphabet.

Which of the following is not a quadratic equation?

Choose the correct alternative answer for the following sub questions and write the correct alphabet.

If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X² + 2X + k = 0

Choose the correct alternative answer for the following sub questions and write the correct alphabet.

What is the value of discriminant for the quadratic equation X² – 2X – 3 = 0?

Choose the correct alternative answer for the following sub-questions and write the correct alphabet.

Which of the following quadratic equation has roots – 3 and – 5?

Choose the correct alternative answer for the following sub questions and write the correct alphabet.

If one of the roots of quadratic equation X² – kX + 27 = 0 is 3, then find the value of ‘k’

Choose the correct alternative answer for the following sub questions and write the correct alphabet.

Degree of quadratic equation is always ______

Write the given quadratic equation in standard form and also write the values of a, b and c

4y² – 3y = – 7

Write the roots of following quadratic equation.

(p – 5) (p + 3) = 0

If a = 1, b = 4, c = – 5, then find the value of b² – 4ac

If b² – 4ac > 0 and b² – 4ac < 0, then write the nature of roots of the quadratic equation for each given case

Write the given quadratic equation in standard form.

m (m – 6) = 9

Complete the following activity to solve the given quadratic equation by factorization method.

Activity: x² + 8x – 20 = 0

x² + ( __ ) – 2x – 20 = 0

x (x + 10) – ( __ ) (x + 10) = 0

(x + 10) ( ____ ) = 0

x = ___ or x = 2

Complete the following activity to find the value of discriminant for quadratic equation 4x² – 5x + 3 = 0.

Activity: 4x² – 5x + 3 = 0

a = 4 , b = ______ , c = 3

b² – 4ac = (– 5)² – (______) × 4 × 3

= ( ______ ) – 48

b² – 4ac = ______

If one of the roots of quadratic equation x² + kx + 54 = 0 is – 6, then complete the following activity to find the value of ‘k’.

Activity: One of the roots of the quadratic equation x² + kx + 54 = 0 is – 6.

Therefore let’s take x = ______

(– 6)² + k(– 6) + 54 = 0

(______) – 6k + 54 = 0

– 6k + ______ = 0

k = ______

To decide whether 1 is a root of quadratic equation x² + 4x – 5 = 0 or not, complete the following activity.

Activity: When x = (______)
L.H.S. = 1² + 4(______) – 5
= 1 + 4 – 5
= (______) – 5
= ______
= R.H.S
Therefore x = 1 is a root of quadratic equation x² + 4x – 5 = 0

Solve the following quadratic equation by factorization method.

3p² + 8p + 5 = 0

If one of the roots of quadratic equation x² – kx – 15 = 0 is – 3, then find the value of ‘k’

If the roots of a quadratic equation are 4 and – 5, then form the quadratic equation

If roots of a quadratic equation 3y² + ky + 12 = 0 are real and equal, then find the value of ‘k’

Roots of a quadratic equation are 5 and – 4, then form the quadratic equation

Complete the following activity to solve the given quadratic equation by formula method.

2x² + 13x + 15 = 0

Activity: 2x² + 13x + 15 = 0

a = (______), b = 13, c = 15

b² – 4ac = (13)² – 4 × 2 × (______)

= 169 – 120

b² – 4ac = 49

x = `(-"b" +- sqrt("b"^2 - 4"ac"))/(2"a")`

x = `(- ("______") +- sqrt(49))/4` 

x = `(-13 +- ("______"))/4`

x = `(-6)/4` or x = `(-20)/4`

x = (______) or x = (______)

Complete the following activity to solve the given word problem. The Sum of squares of two consecutive even natural numbers is 244, then find those numbers.

Activity: Let the first even natural number be x
Therefore its consecutive even natural number will be = (______)
By the given condition,
x² + (x + 2)² = 244
x² + x² + 4x + 4 – (______) = 0
2x² + 4x – 240 = 0
x² + 2x – 120 = 0
x² + (______) – (______) – 120 = 0
x(x + 12) – (______) (x + 12) = 0
(x + 12)(x – 10) = 0
x = (______)/x = 10
But natural number cannot be negative, x = – 12 is not possible.
Therefore first even natural number is x = 10.
Second even consecutive natural number = x + 2 = 10 + 2 = 12.

If the roots of the given quadratic equation are real and equal, then find the value of ‘k’

kx(x – 2) + 6 = 0

Mukund has ₹ 50 more than Sagar. If the product of the amount they have is 15,000, then find the amount each has

Solve the following quadratic equation.

`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 0

Solve the following quadratic equations by formula method.

5m² – 4m – 2 = 0

Solve the following quadratic equations by formula method.

`y^2 + 1/3y` = 2

Form a quadratic equation if the roots of the quadratic equation are `2 + sqrt(7)` and `2 - sqrt(7)`

Present age of mother of Manish is 1 year more than 5 times the present age of Manish. Four years before, if the product of their ages was 22, then find the present age of Manish and his mother

In an orchard there are total 200 trees. If the number of trees in each column is more by 10 than the number of trees in each row, then find the number of trees in each row

If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.

(m – 12)x² + 2(m – 12)x + 2 = 0

Solve the following quadratic equation.

`1/(4 - "p") - 1/(2 + "p") = 1/4`

Sum of the roots of the quadratic equation is 5 and sum of their cubes is 35, then find the quadratic equation

Form a quadratic equation such that one of its roots is 5. Form a quadratic equation for it and write. (For the formation of word problems you can use quantities like age, rupees, or natural numbers.) (Sample solution for the above example is given below students can take another number to form another example)
Solution:
We need one of the solutions of the quadratic equation as 5.
Then we can take another root as any number like a positive or negative number or zero. Here I am taking another root of the quadratic equation as 2.
Then we can form a word problem as below,
Smita is younger than her sister Mita by 3 years (5 – 2 = 3). If the product of their ages is (5 × 2 = 10). Then find their present ages. 
Let the age of Mita be x.
Therefore age of Smita = x – 3 
By the given condition,
x(x – 3) = 10
x² – 3x – 10 = 0