Advertisements
Advertisements
प्रश्न
Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
Advertisements
उत्तर
Given quadratic equation is
px(x – 2) + 6 = 0
⇒ px2 – 2px + 6 = 0
For two equal and real roots
(Discriminant) D = 0
⇒ b2 – 4ac = 0
Here, b = –2p, a = p, c = 6
∴ (–2p)2 – 4 × p × 6 = 0
⇒ 4p2 – 24p = 0
⇒ 4p(p – 6) = 0
⇒ p = 6
APPEARS IN
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2(5 + 2k)x + 3(7 + 10k) = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(4 - k)x2 + (2k + 4)x + 8k + 1 = 0
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
Find the value of k for which the roots of the equation 3x2 - 10x + k = 0 are reciprocal of each other.
If one root of the equation x2+ px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, the value of q is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
If one root of equation (p – 3) x2 + x + p = 0 is 2, the value of p is ______.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
