Question

please answer this question
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Answer 1

Answer:

Given: p(x)=4x²+4–3

To Prove: Value of 'x'=1/2 or –3/2

Let, p(x)=0 [as, x is a root of p(x)]

so, 4x²+4x–3=0

Here, sum of zeroes=4

product of zeroes=–12

so, p(x)=4x²+6x–2x–3=0

2x(2x+3)–1(2x+3)=0

or (2x–1)(2x+3)=0

=> (2x–1)=0 or (2x+3)=0

x=1/2 or x=–3/2

Hence, proved.

Now, Verification of zeroes:

let, ɑ=1/2 and ß=–3/2

sum of zeroes of p(x):

ɑ+ß=–b/a

1/2+(–3/2)=–4/4

–2/2=–1

–1=–1

product of zeroes of p(x):

ɑß=c/a

(1/2)(–3/2)=–3/4

–3/4=–3/4

as, LHS=RHS in both the cases.

Hence, verified