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If alpha and beta are the zeros of the polynomial x2-5x+m such that alpha -beta = 1, find m

Posted by Hemal Ravrani 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Since {tex}\alpha , \beta{/tex} are the zeros of the polynomial f(x) = x² - 5x + m.
Compare f(x) = x² - 5x + m with ax²+ bx + c.
So, a = 1 , b = -5 and c = m
{tex}\alpha + \beta = - \frac { ( - 5 ) } { 1 }{/tex} = 5
{tex}\alpha \beta = \frac { mk } { 1 } = m{/tex}
Given, {tex}\alpha - \beta{/tex} = 1
Now, {tex}( \alpha + \beta ) ^ { 2 } = ( \alpha - \beta ) ^ { 2 } + 4 \alpha \beta{/tex}
{tex}\Rightarrow{/tex} (5)² = (1)² + 4m
{tex}\Rightarrow{/tex} 25 = 1 + 4m
{tex}\Rightarrow{/tex} 4m = 24
{tex}\Rightarrow{/tex} m = 6
Hence the value of m is 6.

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CBSE > Class 10 > Mathematics