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If alpha and beta are zeros …

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If alpha and beta are zeros of quadratic polynomial X square + X - 2 find the value of one upon Alpha minus one upon beta

Posted by Ishita Sharma 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

Since, {tex}α{/tex} and {tex}β{/tex} are the zeroes of the quadratic polynomial.
We have,
f(x) = x² + x - 2
{tex}\Rightarrow{/tex}x² + x - 2 = 0
{tex}\Rightarrow{/tex}x² + 2x - x - 2 = 0
{tex}\Rightarrow{/tex}x(x +2) -1(x + 2) = 0

{tex}\Rightarrow (x-1)(x+2)=0{/tex}

{tex}\Rightarrow x-1=0 \ and \ x+2=0{/tex}
{tex}\Rightarrow{/tex}x = 1 and x = -2
{tex}\therefore \alpha = -2, \beta = 1{/tex}
So,
{tex}\frac{1}{\alpha } - \frac{1}{\beta }{/tex}
{tex}= \frac{{\beta - \alpha }}{{\alpha \beta }}{/tex}
= {tex}\frac{{1 + 2}}{{2(- 1)}} = - \frac{3}{2}{/tex}

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