f (x)=10x^2+3x-4 factorise and find zeroes
Answers
Let 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
.
Therefore, hence verified.
Answer:
Step-by-step explanation:
Refer to that below
