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find the polynomial whose double of zeros of x square minus x minus 6 |
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Answer» x²-x-6 can be written as x²+2x-3x-6, which can be written as 2(x+2) -3(x+2) or (x+2)(x-3). then roots are -2 and 3. then polynomial whose roots are -4 and 6 is x²- (-4+6)x +(-4)(6) = x² -2x -24. Alternatively we know that root1+root2= -b/a -----(i) and root1×root2= c/a -------(ii) then, let the roots of new polynomial be (2A) and (2B), where A and B are roots of x²-x-6 ---------(iii). then new polynomial can be written as x² -(Sum of roots)x + product of roots x² - (2A+2B)x +(2A)(2B) which is x²- 2x(A+B) +4AB -----(iv) from (i),(ii),(iii) A+B =1 and AB= -6 putting in (iv), x² - 2x - 24
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