Advertisements
Advertisements
Question
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
Solution
When x = 1,
L.H.S. = 12 + 4(1) – 5
= 1 + 4 – 5
= 5 – 5
= 0
= R.H.S.
Therefore x = 1 is a root of quadratic equation x2 + 4x – 5 = 0.
RELATED QUESTIONS
If the roots of 2x2 - 6x + k = 0 are real and equal, find k.
Solve : 7y = -3y2 - 4
If α and β are the roots of the quadratice equation x²- 2x - 7= 0, find the
value α² + β²
Form the quadratic equation if the roots are 3 and 8.
If one root of the quadratic, x2 - 7x + k = 0 is 4. then find the value of k.
Solve the quadratic equation : 3x4 - 13x2 +10 = 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’
If the roots of a quadratic equation are 4 and – 5, then form the quadratic equation
Solve the following quadratic equation.
`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 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
Determine whether 2 is a root of quadratic equation 2m2 – 5m = 0.
One of the roots of equation kx2 – 10x + 3 = 0 is 3. Complete the following activity to find the value of k.
Activity:
One of the roots of equation kx2 – 10x + 3 = 0 is 3.
Putting x = `square` in the above equation
∴ `"k"(square)^2 - 10 xx square + 3` = 0
∴ `square` – 30 + 3 = 0
∴ 9k = `square`
∴ k = `square`
If the sum of the roots of the quadratic equation x2 + kx + 6 = 0 is 6, then the value of k is ______.
Show that (x + 1) is a factor of the polynomial `x^3 - x^2 - (2 + sqrt(2))x + sqrt(2)`.
One of the roots of equation x2 + 5x + a = 0 is – 3. To find the value of a, fill in the boxes.
Since, `square` is a root of equation x2 + 5x + a = 0
∴ Put x = `square` in the equation
⇒ `square^2 + 5 xx square + a` = 0
⇒ `square + square + a` = 0
⇒ `square + a` = 0
⇒ a = `square`
Find the roots of the quadratic equation `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0.