Advertisements
Advertisements
प्रश्न
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px2 – 4x + 3 = 0
Advertisements
उत्तर
px2 – 4x + 3 = 0
Here a = p, b = -4, c = 3
∴ D = b2 - 4ac
= (-4)2 - 4 x p x 3
= 16 - 12p
∵ The roots are equal
∴ D = 0
⇒ b2 - 4ac = 0
⇒ 16 - 12p = 0
⇒ 12p = 16
⇒ p = `(16)/(12) = (4)/(3)`
∴ p = `(4)/(3)`.
APPEARS IN
संबंधित प्रश्न
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=0`
Find the positive value(s) of k for which quadratic equations x2 + kx + 64 = 0 and x2 – 8x + k = 0 both will have real roots ?
Solve the following quadratic equation using formula method only
5x2 - 19x + 17 = 0
Solve the following quadratic equation using formula method only
`"x"^2 - 4 sqrt 15 "x" - 4 = 0`
Find the value of k for which the given equation has real roots:
kx2 - 6x - 2 = 0
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.
A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify.
