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Find the quadratic polynomial whose sum of zeroes is 15 and one of the zero is -3.

Dear Student,
Solution) Let α = -3 and let β be the other root.
Now, Sum of zeroes , α + β = 15
                                       ⇒ β = 15 - (- 3) = 15 + 3 = 18.
Product of zeroes, αβ = (- 3) (18) = - 54
Therefore, the required quadratic polynomial is
p(x) = x​​​​​​2 - (sum of zeroes) x + (product of zeroes)
p(x) = x2 - (α+β )x + αβ 
p(x) = x2 - 15x - 54
​​​​​​​Regards!

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f(x) = x^2-15x-54
 
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Let f(x) be a polynomial and its roots be 'a' and 'b'.
Here, a=-3
Now,
f(x)= x? - (sum of roots)x + (product of roots) ( this is the way we can find a quadratic polynomial by using roots. This is a formula and roots = zeros)

? sum of roots = 15
? a+b=15
?(-3)+b=15
?b=18

Also,
product of roots =ab = (18)*(-3)=-54

Hence,
f(x) = x?-15x-54 is the required quadratic equation.
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