Advertisements
Advertisements
Question
If `(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0, find the values of p and q.
Advertisements
Solution
`(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0
Substituting the value of x = and – 3 respectively, we get
`"p"(2/3)^2 + 7(2/3) + "q"` = 0
⇒ `(4)/(9)"p" + (14)/(3) + "q"` = 0
⇒ 4p + 42 + 9q = 0
⇒ 4p + 9q = -42 ...(i)
and
p(-3)2 + 7(-3) + q = 0
9p - 21 + q = 0
⇒ 9p + q = 21 ...(ii)
q = 21 - 9p
Substituting the value of q in (i)
4p + 9(21 - 9p) = -42
4p + 189 - 81p = -42
-77p = -42 - 189 = -231
p = `(-231)/(-77)` = 3
∴ q
= 21 - 9 x 3
= 21 - 27
= -6
∴ p = 3, q = -6.
APPEARS IN
RELATED QUESTIONS
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
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 value of the discriminant in the following quadratic equation:
2x2 - 5x + 3 = 0
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: 2x2 + 15x + 30 = 0
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
Find the roots of the quadratic equation by using the quadratic formula in the following:
`1/2x^2 - sqrt(11)x + 1 = 0`
If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.
