Question

Find the zeroes of the polynomial p(x) = 3x² + x – 10 and verify the relationship between zeroes and its coefficients.

Answer 1

P(x) = 3x²+x-10

3x²+x-10 = 3x²+6x-5x-10

= 3x(x+2) - 5 (x+2)

= (3x-5)(x+2)

3x-5 = 0 or x+2 = 0

\(\therefore\) \(x = \frac{5}{3}\) and  x = -2

Therefore, zeroes of 3x² + x – 10 are –2 and \(\frac{5}{3}\)

Verification : 

Sum of zeroes \(= -2+\frac{5}{3} = \frac{-6+5}{3} = \frac{-1}{3} = - \frac{-(coeff.\space of\space x)}{coeff.\space of\space x^2}\)

Product of zeroes \(= (-2) × \left( \frac{5}{3}\right) = - \frac{10}{3} = \frac{Constant \space term}{coeff.\space of \space x^2}\)

Hence verified