Find the zeroes of the polynomial by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials 4x^2 - 3x - 1
Answers
Answer:
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Answer:
3Let f(x)=3x
2
+4x−4
Comparing it with the standard quadratic polynomial ax
2
+bx+c, we get
a=3, b=4, c=−4
Now, 3x
2
+4x−4
=3x
2
+6x−2x−4
=3x(x+2)−2(x+2)
=(x+2)(3x−2)
The zeros of f(x) are given by f(x)=0
=>(x+2)(3x−2)=0
=>x+2=0,3x−2=0
=>x=−2,x=
3
2
Hence the zeros of the given quadratic polynomial are −2,
3
2
Verification of the relationship between the roots and the coefficients
Sum of the roots =−2+
3
2
=
3
−6+2
=
3
−4
=
coefficientofx
2
−coefficientofx
Product of the roots =−2×(
3
2
)
=
3
−4
=
coefficientofx
2
constantterm
Step-by-step explanation:
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