The zeroes of the polynomial $f (x) = x^{2} - 5 x^{2} - 2 x + 24$ , if it is given that the product of its two zeroes is $12$ are_________.

3, 4, - 2

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- 3, - 4, - 2

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3, - 4, - 2

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3, 4, 2

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Solution

The correct option is A $3, 4, - 2$
$x^{3} - 5 x^{2} - 2 x + 24 = 0$

$x^{3} - 7 x^{2} + 2 x^{2} - 14 x + 12 x + 24 = 0$

$x (x^{2} - 7 x + 12) + 2 (x^{2} - 7 x + 12) = 0$

$(x + 2) (x^{2} - 7 x + 12) = 0$

$(x + 2) (x^{2} - 4 x - 3 x + 12) = 0$

$(x + 2) (x (x - 3) - 4 (x - 3) = 0$

$(x + 2) (x - 3) (x - 4) = 0$

The roots are $- 2, 3, 4$

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The zeroes of the polynomial f(x)=x2−5x2−2x+24, if it is given that the product of its two zeroes is 12 are_________.

The correct option is A 3,4,−2x3−5x2−2x+24=0x3−7x2+2x2−14x+12x+24=0x(x2−7x+12)+2(x2−7x+12)=0(x+2)(x2−7x+12)=0(x+2)(x2−4x−3x+12)=0(x+2)(x(x−3)−4(x−3)=0(x+2)(x−3)(x−4)=0The roots are −2,3,4

The zeroes of the polynomial $f (x) = x^{2} - 5 x^{2} - 2 x + 24$ , if it is given that the product of its two zeroes is $12$ are_________.