Advertisements
Advertisements
प्रश्न
If `(2)/(3)` and – 3 are the roots of the equation px2+ 7x + q = 0, find the values of p and q.
Advertisements
उत्तर
`(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
संबंधित प्रश्न
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 0
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
`sqrt(3)x^2 + 11x + 6sqrt(3)` = 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
Find the nature of the roots of the following quadratic equations: `x^2 - 2sqrt(3)x - 1` = 0 If real roots exist, find them.
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.
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`sqrt(2)x^2 - 3/sqrt(2)x + 1/sqrt(2) = 0`
Every quadratic equations has at most two roots.
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
For the roots of the equation a – bx – x2 = 0; (a > 0, b > 0), which statement is true?
