Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients X square + 15 X + 54
please answer my ​

Answer 1

Answer :

The zeroes of the polynomial are -6 and -9

Given :

The quadratic polynomial is :

• $\sf{x^{2} + 15x + 54}$

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

$\sf{\implies -6+( - 9) = -\dfrac{15}{1} }\\\\ \sf{\implies -6 -9 = -15 }\\\\ \bf{\implies -15 = -15}$

Product of the zeroes = constant term/coefficient of x²

$\sf{\implies (-6)(-9) = \dfrac{54}{1}}\\\\ \bf{\implies 54 = 54}$

Hence Verified