19. Find a quadratic polynomial whose zeroes are -12 and 4 and verify the relationship between the
zeroes and the coefficiens.
Answers
Answer:
quadratic polynomial is x
2
+2x−3
Step-by-step explanation:
Given that 1 and -3 are the zeroes of quadratic polynomial.
we have to find the quadratic polynomial and also verify the relation between the coefficients and zeros of the polynomial.
As 1 and -3 are zeroes
∴ (x-1) and (x+3) are factors
⇒ The quadratic polynomial is
(x-1)(x+3)=x(x+3)-1(x+3)(x−1)(x+3)=x(x+3)−1(x+3)
=x^2+3x-x-3=x
2
+3x−x−3
=x^2+2x-3=x
2
+2x−3
which is required polynomial.
Verification:
\text{sum of zeroes=}\frac{-b}{a}=\frac{-2}{1}sum of zeroes=
a
−b
=
1
−2
\alpha+\beta=-2α+β=−2
1+(-3)=-21+(−3)=−2
-2=-2−2=−2 Verified
\text{product of zeroes=}\frac{c}{a}=\frac{-3}{1}product of zeroes=
a
c
=
1
−3
\alpha.\beta=-3α.β=−3
1.(-3)=-31.(−3)=−3
-3=-3−3=−3 Verified