Question

Find the zeros of the polynomial x2 +2x-15,and verify the relationship between the zeroes and coefficients

Answer 1

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p(x) = ${x}^{2} + 2x - 15 = 0$

p(x) = 0

$\therefore{ {x}^{2} + 2x - 15 = 0} \\ \\ = > {x}^{2} + (5 - 3)x - 15 = 0 \\ \\ = > {x}^{2} + 5x - 3x - 15 = 0 \\ \\ = > x(x + 5) - 3(x + 5) = 0 \\ \\ = > (x + 5)(x - 3) = 0$

x = -5 and x = 3


VERIFICATION

$sum \: of \: the \: zeroes \: = \frac{ - b}{a} \\ \\ = > - 5 + 3 = \frac{ - 2}{1} \\ \\ = > - 2 = - 2 \\ \\ again \\ \\ product \: of\: the \: zeroes \: = \frac{c}{a} \\ \\ = > - 5 \times 3 = \frac{ - 15}{1} \\ \\ = > - 15 = - 15$
verified


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Answer 2

Answer:

Here's your answer

${x}^{2} + 2x - 15 \\ \\ {x}^{2} - 3x + 5x - 15 \\ \\ x(x - 3) + 5(x - 3) \\ \\ (x - 3)(x + 5) \\ \\ verification \\ \\ \alpha + \beta = \frac{ - b}{a}$

$\alpha = 3 \: and \: \beta = - 5 \\ \\ \alpha + \beta = - 2 \\ \\ 3 - 5 = - 2 \\ \\ - 2 = - 2$

$\alpha \beta = \frac{c}{a} \\ \\ 3 \times - 5 = - 15 \\ \\ - 15 = - 15 </strong><strong>$

Hence verified

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