Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients of the polynomial: x²+2√5x - 15​

Answer 1

Step-by-step explanation:

${x}^{2} + 2 \sqrt{5}x - 15 = 0 \\ \\ {x}^{2} + 3 \sqrt{5} x - \sqrt{5} x - 15 = 0 \\ \\ x(x + 3 \sqrt{5} ) - \sqrt{5} (x + 3 \sqrt{5} ) = 0 \\ \\ (x - \sqrt{5} )(x + 3 \sqrt{5} ) = 0 \\ \\ \alpha = \sqrt{5} \: \: \: \: \: \: \: \: \: \: \: \: \beta = - 3 \sqrt{5} . \\ \\ \alpha + \beta = - 2 \sqrt{5} \\ \\ \alpha \beta = - 15 \\ \\ also \: \: \: \: \alpha + \beta = - \frac{coefficient \: of \: x}{coefficient \: of \: {x}^{2} } = \frac{ - 2 \sqrt{5} }{1} \\ \\ \alpha \beta = \frac{constant \: term}{coefficient \: of \: {x}^{2} } = \frac{ - 15}{1} .$