1.

If 2 and -3 are the zeroes of the followingquadratic polynomial, then find the value of aand bx2 + (a + 1) x + b

Answer»

Answer

The REQUIRED values are

a = 0

b = -6

\bf \large \underline{Given : }

The quadratic polynomial

  • x² + (a + 1)x + b
  • 2 and -3 are the zeroes of the given polynomial

\bf \large \underline{To \: Find : }

\bf \large \underline{Solution : }

The zeroes of the polynomial x² + (a + 1)x + b are 2 and -3 .

Thus , from the RELATIONSHIP of SUM of zeroes and coefficients we have ,

\sf sum \: of \: the \: zeroes = \dfrac{coefficients \: of \: x}{coefficient\: of \: x^{2}} \\\\ \sf\implies 2 + (-3) = -\dfrac{a + 1}{1} \\\\ \sf\implies -1 = -a - 1 \\\\ \sf\implies -a = -1+1 \\\\ \sf \implies a = 0

Again, from the relationship of product of the zeroes and coefficients of the polynomial ,

\sf product \: of \: the \: zeroes = \dfrac{constant \: term}{coefficient \: of \: {x}^{2} }

\sf\implies (2)(-3) = \dfrac{b}{1} \\\\ \sf\implies -6 = b \\\\ \sf\implies b = -6

Therefore , required value of a and b are 0 and -6 RESPECTIVELY.



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