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
Determine the nature of the roots of the following quadratic equation :
2x2 + x-1=0
Solve for x: (x2 - 5x)2 - 7(x2 - 5x) + 6 = 0; x ∈ R.
In each of the following, determine whether the given numbers are roots of the given equations or not; 6x2 – x – 2 = 0; `(-1)/(2), (2)/(3)`
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
If α + β = 4 and α3 + β3 = 44, then α, β are the roots of the equation:
If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify.
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
