find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients X square + 15 X + 54
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Answer :
The zeroes of the polynomial are -6 and -9
Given :
The quadratic polynomial is :
Task :
- To find the zeroes of the quadratic polynomial.
- To verify the relationship between the zeroes and the coefficients of the polynomial
Solution :
Splitting the middle term of the given polynomial :
x² + 6x + 9x + 54
= x(x + 6) + 9(x + 6)
= (x + 6)(x + 9)
Therefore , the zeroes are :
x + 6 = 0 and x + 9 = 0
⇒x = -6 and ⇒x = -9
______________________
Verification of the relationship between zeroes and the coefficients
Sum of the zeroes = -coefficient of x/coefficient of x²
Product of the zeroes = constant term/coefficient of x²
Hence Verified
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