Advertisements
Advertisements
Question
Solve using formula.
5m2 – 4m – 2 = 0
Solution
5m2 – 4m – 2 = 0 compare with ax2 + bx + c = 0, we get
⇒ a = 5, b = – 4 and c = - 2
∴ b2 - 4ac = (- 4)2 - 4 (5)(- 2)
= 16 - (-40)
= 16 + 40
= 56
We have the formula,
`m = (-b ± sqrt(b^2 - 4ac))/(2a)`
Substituting the values in the formula, we get,
⇒ m = `(-(-4) ± sqrt(56))/(2 xx 5)`
⇒ m = `(4 ± sqrt(4 xx 14))/(2 xx 5)`
⇒ m = `(4 ± 2sqrt(14))/(2 xx 5)`
⇒ m = `(2(2 ± sqrt14))/(2 xx 5)`
⇒ m = `(2 ± sqrt 14)/(5)`
The roots are
⇒ `m = (4 + 2sqrt(14))/10 "or" m = (4 - 2sqrt(14))/10`
⇒ `m = (2 + sqrt(14))/5 "or" m = (2 - sqrt(14))/5`
RELATED QUESTIONS
Compare the given quadratic equation to the general form and write values of a,b, c.
2m2 = 5m – 5
Solve using formula.
x2 + 6x + 5 = 0
Solve using formula.
y2 + `1/3`y = 2.
With the help of the flow chart given below solve the equation \[x^2 + 2\sqrt{3}x + 3 = 0\] using the formula.
The roots of the following quadratic equation is real and equal, find k.
3y2 + ky +12 = 0
The roots of the following quadratic equation is real and equal, find k.
kx (x – 2) + 6 = 0
Find the value of discriminant of the following equation.
5m2 - m = 0
One of the roots of quadratic equation \[2 x^2 + kx - 2 = 0\] is –2. find k.
Two roots of quadratic equation is given ; frame the equation.
0 and 7
Determine the nature of root of the quadratic equation.
\[3 x^2 - 5x + 7 = 0\]
Determine the nature of root of the quadratic equation.
\[\sqrt{3} x^2 + \sqrt{2}x - 2\sqrt{3} = 0\]
The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.
Find quadratic equation such that its roots are square of sum of the roots and square of difference of the roots of equation \[2 x^2 + 2\left( p + q \right)x + p^2 + q^2 = 0\]
If α and β are the roots of the equation is 3x2 + x – 10 = 0, then the value of `1/α + 1/β` is ______.
If 2 and 5 are the roots of the quadratic equation, then complete the following activity to form quadratic equation:
Activity:
Let α = 2 and β = 5 are the roots of the quadratic equation.
Then quadratic equation is:
x2 − (α + β)x + αβ = 0
∴ `x^2 - (2 + square)x + square xx 5 = 0`
∴ `x^2 - square x + square = 0`
