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Find a quadratic polynomial whose zeroes...

Find a quadratic polynomial whose zeroes are -2 and 5. Hence, verify the relation between zeroes and coefficients of the polynomial.

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Let `alpha`=-2 and `beta`=5 be the zeroes of the polynomial p(x).
`:." " p(x)=x^(2)-(alpha+beta)x+alphabeta=x^(2)-(-2+5)x+(-2)(5)`
`=x^(2)-3x-10 " "` Ans.
Now, sum of zeroes`=alpha+beta`
=-2+5=3
`=-(-3)/(1)=-("coefficient of" x)/("coefficient of" x^(2))`
and product of zeroes `=alphabeta`=(-2)(5)
=-10=`(10)/(1)=("coefficient of term")/("coefficient of "x^(2)) " "` Hence Verified.
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