Advertisements
Advertisements
Question
Without solving the following quadratic equation, find the value of ‘p’ for which the roots are equal.
px2 – 4x + 3 = 0
Advertisements
Solution
px2 – 4x + 3 = 0
Here a = p, b = −4 and c = 3
Given equation has equal roots
Then D = 0
`=>` b2 – 4ac = 0
`=>` [–4]2 – 4(p)(3) = 0
`=>` 16 – 12p = 0
`=>` –12p = –16
`=> p = (-16)/(-12) = 4/3`
APPEARS IN
RELATED QUESTIONS
For what value of m, are the roots of the equation (3m + 1)x2 + (11 + m) x + 9 = 0 equal?
Find the value of k for which the equation x2 + k(2x + k – 1) + 2 = 0 has real and equal roots.
Determine the nature of the roots of the following quadratic equation:
9a2b2x2 – 24abcdx + 16c2d2 = 0, a ≠ 0, b ≠ 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
If a = 1, b = 8 and c = 15, then find the value of `"b"^2 - 4"ac"`
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’.
The sum of the roots of the quadratic equation 3x2 – 9x + 5 = 0 is:
