Advertisements
Advertisements
Question
Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
Advertisements
Solution
We have
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
Here, `a = (4)/(3), b = -2 and c = (3)/(4)`
Discriminant
= b2 - 4ac
= (-2)2 -4 x `(4)/(3) xx (3)/(4)`
= 4 - 4
= 0
So, the given equation has two real and equal roots given by
a = `(-b + sqrt(b^2 - 4ac))/(2a)`
= `(+ 2 + 0)/(4)`
= `(3)/(4)`
and β = `(-b - sqrt(b^2 - 4ac))/(2a)`
= `(+ 2 - 0)/(2 xx (4)/(3))`
= `(3)/(4)`.
RELATED QUESTIONS
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
In each of the following determine the; value of k for which the given value is a solution of the equation:
3x2 + 2kx - 3 = 0; x = `-(1)/(2)`
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
If 4 is a root of equation x2 + kx – 4 = 0; the value of k is ______.
