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Find the zeros of the quadratic …

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Find the zeros of the quadratic pilynomial x^2+7x+10 and verify the relationship between zeros and coefficient

Posted by Aabith $ 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

The zeros of f(x) are given by f(x) = 0
{tex} \Rightarrow {/tex}x² + 7x + 10 = 0
{tex}\Rightarrow {/tex}(x + 5)(x + 2) = 0
{tex}\Rightarrow {/tex} x + 5 = 0 or, x + 2 = 0
{tex}\Rightarrow {/tex} x = -5 or, -2
Thus, the zeroes of f(x) = x² +7x + 12 are {tex}\alpha = - 5 \text { and } \beta = - 2{/tex}

{tex}\alpha + \beta{/tex}= (-5) + (-2) = -7.......(1)

and {tex}\alpha\beta=(-5)(-2)=10.….....(2){/tex}

In the eqn x² +7x+10=0

a=1,b=7,c=10

So {tex}\alpha +\beta =\frac{-b}{a}=\frac{-7}{1}=-7..........(3){/tex}

and {tex}\alpha\beta=\frac ca=\frac{10}{1}=10........(4)..{/tex}

Hence from (1) and (3) sum of zeros and from (2) ,and (4) product of zeros is verified.

0Thank You

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