Advertisements
Advertisements
प्रश्न
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x2 + (p – 3)x + p = 0.
Advertisements
उत्तर
x2 + (p – 3)x + p = 0
Here a = 1, b = (p - 3), c = p
∵ Equation has real and equal roots
∴ b2 - 4ac = 0
⇒ (p - 3)2 - 4(1)(p) = 0
⇒ (p - 3)2 - 4p = 0
⇒ p2 + 9 - 6p - 4p = 0
⇒ p2 - 10p + 9 = 0
⇒ p2 - 9p - p + 9 = 0
⇒ p(p - 9) -1(p - 9) = 0
⇒ (p - 1)(p - 9) = 0
∴ p = 1, 9
APPEARS IN
संबंधित प्रश्न
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
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
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
Which of the following equations has the sum of its roots as 3?
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 0
Every quadratic equation has at least one real root.
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?
If 3 is a root of the quadratic equation x2 – px + 3 = 0, then p is equal to ______.
