4. The sum of the zeroes of a quadratic polynomial is 15 4 and their product Question 4. The sum of the zeroes of a quadratic polynomial is 15 4 and their product in progress 0 Math Emery 1 month 2021-08-17T15:59:15+00:00 2021-08-17T15:59:15+00:00 1 Answer 0 views 0

## Answers ( )

Answer:ATQ

\alpha + \beta = \frac{15}{4}

\alpha \beta = 3

We know that the polynomial is of the form

P(x) = x^{2} – (\alpha + \beta)x + \alpha \beta

P(x) = x^{2} – (\frac{15}{4} )x + 3

P(x) = x^{2} – \frac{15x}{4} + 3

P(x) = \frac{4x^{2} – 15x + 12}{4}

As we know that P(x) is always equal to 0

Therefore

0 = \frac{4x^{2} – 15x + 12}{4}

0 = 4x^{2} – 15x + 12

Therefore the polynomial is P(x) = 4x^{2} – 15x + 12