Advertisements
Advertisements
Question
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Advertisements
Solution
- a = p
- b = `-2sqrt5p`
- c = 15
Δ = b2 − 4ac
`(−2sqrt5p)^2−4(p)(15)=0`
`(2sqrt5p)^2 - 60p = 0`
4 × 5p2 − 60p = 0
20p2 − 60p = 0
20p(p − 3) = 0
p = 0 or p = 3
Since p = 0 would make the equation invalid, we take:
p = 3
APPEARS IN
RELATED QUESTIONS
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(3k + 1)x + 8k + 1 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
x2 - kx + 9 = 0
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
Write the discriminant of the quadratic equation (x + 5)2 = 2 (5x − 3).
In the quadratic equation kx2 − 6x − 1 = 0, determine the values of k for which the equation does not have any real root.
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
Find the value of ‘k’ for which the quadratic equation 2kx2 – 40x + 25 = 0 has real and equal roots.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal.
Prove that 2q = p + r; i.e., p, q, and r are in A.P.
