Advertisements
Advertisements
Question
Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0
Advertisements
Solution
x² + (p – 3) x + p = 0
Here a = 1, b = p - 3, c = p
For real and equal roots
D = b2 - 4ac = 0
(p - 3)2 - 4 x 1 x p = 0
p2 - 6p + 9 - 4p = 0
p2 - 10p + 9 = 0
⇒ p2 - p - 9 (p - 1) = 0
p(p - 1) - 9 (p - 1) = 0
⇒ (p - 1) (p - 9) = 0
⇒ p = 1 or p = + 9
RELATED QUESTIONS
Determine the nature of the roots of the following quadratic equation:
9a2b2x2 - 24abcdx + 16c2d2 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
If the roots of the equations ax2 + 2bx + c = 0 and `bx^2-2sqrt(ac)x+b = 0` are simultaneously real, then prove that b2 = ac.
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
If b and c are odd integers, then the equation x2 + bx + c = 0 has ______.
The number of integral values of m for which the equation (1 + m2)x2 – 2(1 + 3m)x + (1 + 8m) = 0 has no real root is ______.
