If x-2 and x-1 - 2 are the factors of the polynomial q x2-5 x-p- then find the relation between p and q

The correct option is A p = qLet f(x) = qx2+5x+p Since x 2 is a factor therefore f(2) = 0 by factor theorem q(22) + 5(2) + p = 0 4q + p = 10 ........(i) ...

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Standard X

Mathematics

Factor Theorem

If x-2 and x-...

Question

If (x-2) and (x-¹/₂) are the factors of the polynomial qx²+5x+p, then find the relation between p and q.

p = q

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p ≠ q

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p < q

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p > q

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Solution

The correct option is A
p = q

Let f(x) = qx²+5x+p
Since x - 2 is a factor therefore f(2) = 0 by factor theorem
q(2²) + 5(2) + p = 0
4q + p = - 10 ........(i)

Since x - is a factor therefore f() = 0 by factor theorem
q() ² + 5() + p = 0
+ p = - 5/2 .....(ii)

(i) - (ii)
4q - = - 10 + 5/2
16q - q = - 40 + 10
15 q = - 30
q = - 2
Substituting in (i)
4(- 2) + r = - 10
p = - 10 + 8
p = - 2
Therefore, p = q = -2

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If (x-2) and (x-1/2) are the factors of the polynomial qx2+5x+p, then find the relation between p and q.

If (x-2) and (x-¹/₂) are the factors of the polynomial qx²+5x+p, then find the relation between p and q.