Find the zeroes of the quadratic polynomial 4x^2−4x−3 and verify the relationship between the zeroes and the coefficients of the polynomial.

nestalno4szl

nestalno4szl

Answered question

2023-02-20

Find the zeroes of the quadratic polynomial 4x2-4x-3 and verify the relationship between the zeroes and the coefficients of the polynomial.

Answer & Explanation

Leonard Drake

Leonard Drake

Beginner2023-02-21Added 6 answers

Step 1: Form the equation
The given polynomial is 4x2-4x-3
We are aware that a polynomial's zeroes are evaluated by equating them to zero.
px=0
4x2-4x-3=0
Step 2: Solve to find the zeroes
4x2-4x-3=0
4x2-6x+2x-3=0
2x2x-3+12x-3=0
2x-32x+1=0
x=32,-12
Step 3: Verification
We know that for a given polynomial ax2+bx+c,
Sum of the zeroes=-ba and product of the roots=ca
Sum of the zeroes =32-12=1
Again, -ba=44=1
Product of the zeroes =32×-12=-34
Again, ca=-34
As a result, the polynomial's zeroes and coefficients are proven to be related.
Hence, the zeroes of this polynomial are 32 and -12.

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