Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
Solve the following quadratic equation using formula method only
15x2 - 28 = x
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:
If the roots of the equations ax2 + 2bx + c = 0 and `"bx"^2 - 2sqrt"ac" "x" + "b" = 0` are simultaneously real, then
Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 0
Every quadratic equations has at most two roots.
