Find the value of the constants a and b, if (x - 2) and (x + 3) are both factors of the expression x³ + ax² + bx - 12.
Factorisation
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Question

Find the value of the constants a and b, if (x - 2) and (x + 3) are both factors of the expression x³ + ax² + bx - 12.

KnowledgeBoat · Accepted Answer

f(x) = x³ + ax² + bx - 12 If (x - 2) and (x + 3) or (x - (-3)) are factors of f(x) then, f(2) and f(-3) = 0. On dividing equation by 2, Putting value of b = 2 - 2a from equation 1, Hence, the value of a is 3 and that of b is -4.

Mathematics

Find the value of the constants a and b, if (x - 2) and (x + 3) are both factors of the expression x³ + ax² + bx - 12.

Factorisation

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Find the value of the constants a and b, if (x - 2) and (x + 3) are both factors of the expression x3 + ax2 + bx - 12.

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(i) Find the value of p.
(ii) with this value of p, factorise the above expression completely.

What number should be subtracted from 2x³ - 5x² + 5x so that the resulting polynomial has 2x - 3 as a factor?

If (x + 2) and (x + 3) are factors of x³ + ax + b, find the values of a and b.

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