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- Given that x -1 is a factor of f(x) = ax'+ bx- x+ 2, a, b ER, find the values of a and b. hence olve completely the equation f(x) = 0

- Given that x -1 is a factor of f(x) = ax'+ bx- x+ 2, a, b ER, find the values of a and b. hence olve completely the equation f(x) = 0

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter13: Conic Sections
Section13.1: Circles
Problem 48PS
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Solve Q1 & 2 showing clearly all steps involved

Y. Given that x² - 1 is a factor of f(x) = ax'+ bx² – x + 2, a, b ER, find the values of a and b. hence solve completely the equation f(x) = 0 G(x) = x' + px² + qx + r, when G(x) is divided by (x2 - 4) the remainder is (5x + 10). When it is divided by (x - 1), the remainder is 9. Find the values of the real constants p, q, r. hence show that (x+2) is a factor of G(x) and solve the equation g(x) = 0 completely. (i) Form a cubic equation with real coefficients which has 1-I and 2 as tow of its roots. (ii) when the polynomial f(x) = x'+ ax + bx + c is divided by (x-1), (x+2), (x - 3) the remainders are:-8, 4, 24 respectively. Find the value of a, b and c. show that when f(x) is divided by (x+3) the remainde is zero. Hence solve completely the equation f(x) = 0 2 | x+2 4, Given that g(x) = x'+ x +2x +2,f(x) Given that (x-2) is a factor of f(x), where f(x) = x’ + ax² – x + 2, find the value of a. hence, show that x +1 is a factor of g(x). g(x) 3 factorise f(x) completely.
Transcribed Image Text:Y. Given that x² - 1 is a factor of f(x) = ax'+ bx² – x + 2, a, b ER, find the values of a and b. hence solve completely the equation f(x) = 0 G(x) = x' + px² + qx + r, when G(x) is divided by (x2 - 4) the remainder is (5x + 10). When it is divided by (x - 1), the remainder is 9. Find the values of the real constants p, q, r. hence show that (x+2) is a factor of G(x) and solve the equation g(x) = 0 completely. (i) Form a cubic equation with real coefficients which has 1-I and 2 as tow of its roots. (ii) when the polynomial f(x) = x'+ ax + bx + c is divided by (x-1), (x+2), (x - 3) the remainders are:-8, 4, 24 respectively. Find the value of a, b and c. show that when f(x) is divided by (x+3) the remainde is zero. Hence solve completely the equation f(x) = 0 2 | x+2 4, Given that g(x) = x'+ x +2x +2,f(x) Given that (x-2) is a factor of f(x), where f(x) = x’ + ax² – x + 2, find the value of a. hence, show that x +1 is a factor of g(x). g(x) 3 factorise f(x) completely.
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