2. Find the zeroes of a quadratic polynomial 2x°-2V2x-3 by factorization method and verify the
relations between the zeroes and coefficients of the polynomial.
Answers
Answer:
2x2 +(7/2)x +3/4 The equation can also be written as, 8x2+14x+3 Splitting the middle term, we get, 8x2+12x+2x+3 Taking the common factors out, we get, 4x (2x+3) +1(2x+3) On grouping, we get, (4x+1)(2x+3) So, the zeroes are, 4x+1=0 ⇒ x = -1/4 2x+3=0 ⇒ x = -3/2 Therefore, zeroes are -1/4 and -3/2 Verification: Sum of the zeroes = – (coefficient of x) ÷ coefficient of x2 α + β = – b/a (- 3/2) + (- 1/4) = – (7)/4 = – 7/4 = – 7/4 Product of the zeroes = constant term ÷ coefficient of x2 α β = c/a (- 3/2)(- 1/4) = (3/4)/2 3/8 = 3/8Read more on Sarthaks.com - https://www.sarthaks.com/878325/find-zeroes-the-polynomial-and-verify-relation-between-coefficients-zeroes-polynomial
Step-by-step explanation:
Let f(x)=2x
2
+
2
7
x+
4
3
.
Comparing it with the standard quadratic polynomial ax
2
+bx+c, we get,
a=2, b=
2
7
, c=
4
3
.
Now, 2x
2
+
2
7
x+
4
3
=2x
2
+
2
6
x+
2
1
x+
4
3
=2x(x+
2
3
)+
2
1
(x+
2
3
)
=(x+
2
3
)(2x+
2
1
).
The zeros of f(x) are given by f(x)=0.
=>(x+
2
3
)(2x+
2
1
)=0
=>(x+
2
3
)=0 or (2x+
2
1
)=0
=>x=−
2
3
or x=−
4
1
.
Hence the zeros of the given quadratic polynomial are −
2
3
, −
4
1
.
Verification of the relationship between the roots and the coefficients:
Sum of the roots =(−
2
3
)+(−
4
1
)
=−
4
7
=−
2×2
7
=
coefficientofx
2
−coefficientofx
.
Product of the roots =(−
2
3
)(−
4
1
)
=−
8
3
=−
4×2
3
=
coefficientofx
2
constantterm
.
Hence, verified.