Advertisements
Advertisements
Question
Find the value(s) of p for which the quadratic equation (2p + 1)x2 – (7p + 2)x + (7p – 3) = 0 has equal roots. Also find these roots.
Advertisements
Solution
The quadratic equation given is (2p + 1)x2 – (7p + 2)x + (7p – 3) = 0
Comparing with ax² + bx + c = 0, we have
a = 2p + 1, b = -(7p + 2), c = (7p - 3)
D = b2 - 4ac
⇒ 0 = [-(7p + 2)]2 -4(2p + 1)(7p - 3)
0 = 49p2 + 4 + 28p - 4(14p2 - 6p + 7p - 3)
0 = 49p2 + 4 + 28p - 56p2 - 4p + 12
0 = -7p2 + 24p + 16
0 = -7p2 + 28p - 4p + 16
0 = -7p(p - 4) -4(p - 4)
0 = (-7p - 4)(p - 4)
⇒ -7p - 4 = 0 or p - 4 = 0
Hence, the value of p = `(-4)/(7)` or p = 4.
APPEARS IN
RELATED QUESTIONS
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Find the value of the discriminant in the following quadratic equation :
x2 +2x+4=0
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Find the value(s) of p for which the equation 2x2 + 3x + p = 0 has real roots.
The roots of the quadratic equation 6x2 – x – 2 = 0 are:
The equation 2x2 + kx + 3 = 0 has two equal roots, then the value of k is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Every quadratic equation has at least two roots.
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
Which of the following equations has two real and distinct roots?
