Question

If alpha and beta are the zeros of the quadratic polynomial f (x)= ax2+bx+c, then evaluate α-β
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Answer 1

answer is..............

Answer 2

Answer:

Sum of zeroes = -b/a

α + β = -b/a

Product of zeroes = c/a

αβ = c/a

We know that;

$( \alpha - \beta ) {}^{2} = ( \alpha + \beta ) {}^{2} - 4 \alpha \beta \\ \\ ( \alpha - \beta ) {}^{2} =( \frac{ - b}{a} ) {}^{2} - 4 \times \frac{c}{a} \\ \\ ( \alpha - \beta ) {}^{2} = \frac{b {}^{2} }{a {}^{2} } - \frac{4c}{a} \\ \\ ( \alpha - \beta ) {}^{2} = \frac{b^{2} - 4ac }{a {}^{2} } \\ \\ \alpha - \beta = \pm\sqrt{ \frac{b {}^{2} - 4ac }{a {}^{2} } }$