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
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Find the discriminant of the following equations and hence find the nature of roots: 7x2 + 8x + 2 = 0
Discuss the nature of the roots of the following equation: `sqrt(3)x^2 - 2x - sqrt(3)` = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 4)2 – 8x = 0
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
