Question

$\sf x^2-6x+8=0$

Find both zeros of the polynomial.

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Answer 1

Answer:

Zeros of the polynomial

x² -6x + 8 are

4 and 2

Step-by-step explanation:

x² -6x + 8 = 0

=> x² -4x -2x + 8 = 0

=> x(x -4) -2(x -4) = 0

=> (x -4) (x -2) = 0

(x -4) = 0

=> x = 4

(x -2) = 0

=> x = 2

Answer 2

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Given :-

• $\sf x^2-6x+8=0$

To Find :-

• The zeros of $\sf x^2-6x+8=0$

Solution :-

✰ To find the roots of the given quadratic equation split the terms in to sum of the terms given.

$\qquad$ $\longmapsto\sf x^2-6x+8=0$

$\qquad$ $\longmapsto {\sf {{x}^{2} - 4x - 2x +8 = 0 } }$

✰ Now, take the common terms and find the factors.

$\qquad$ $\longmapsto {\sf {x ( x - 4 ) - 2 ( x - 4 ) = 0 } }$

$\qquad$ $\red\longmapsto {\red{\sf {(x-4)(x-2)=0}}}$

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$\qquad$ $\longmapsto{\sf {(x - 4) = 0}}$

$\qquad$ $\longmapsto{\sf {x - 4 = 0}}$

$\qquad$ ${\color {magenta}\longmapsto}~{\color {magenta}{\sf {x = 4}}}$

$\qquad$ $\longmapsto {\sf {(x - 2) = 0}}$

$\qquad$ $\longmapsto{\sf {x - 2 = 0}}$

$\qquad$ ${\color {magenta}\longmapsto}~{\color {magenta}{\sf {x = 2}}}$

${\sf {\color {coral}{The~ zeros~ are~ 4, 2}}}$

★ Therefore, by the factorization method the roots 4, 2 are the zeros of the quadratic equation $\sf x^2-6x+8=0$ .

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