Find the zeros of the following quadratic polynomials 6x^2-3-7x and verify the relationship between the zeros and the coefficients.

Luis Wolf

Luis Wolf

Answered question

2023-02-06

Find the zeros of the following quadratic polynomials 6x2-3-7x and verify the relationship between the zeros and the coefficients.

Answer & Explanation

CeatMessysga

CeatMessysga

Beginner2023-02-07Added 5 answers

Step 1: Form the equation
The given polynomial is 6x2-3-7x.
We know that the zeroes of a polynomial are evaluated by equating them with zero.
px=0
6x2-7x-3=0
Step 2: Solve to find the zeroes
6x2-7x-3=0
6x2-9x+2x-3=0
3x2x-3+12x-3=0
2x-33x+1=0
x=32,-13
Step 3: Verification
You know that for a given polynomial ax2+bx+c,
Sum of the zeroes=-ba and product of the roots=ca
Sum of the zeroes =32-13=9-26=73
Again, -ba=--76=73
Product of the zeroes =32×-13=-36=-12
Again, ca=-36=-12
Therefore, the relationship between the zeroes and the polynomial coefficients is established.
Thus, the zeroes of this polynomial are 32 and -13.

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