Question

If α and β are the zeroes of the polynomial x2 – 7x – 10, then form a quadratic polynomial whose zeroes are half the zeroes of the given polynomial.​

Answer 1

Answer:

$2 {x}^{2} - 7x - 5 = 0.$

Step-by-step explanation:

$\alpha + \beta = \frac{7}{1} \\ \\ \frac{ \alpha }{2} + \frac{ \beta }{2} = \frac{7}{2} \\ \\ \frac{ \alpha \beta }{1} = - 10 \\ \\ \frac{ \alpha \beta }{4} = - \frac{5}{2} \\ \\ required \: equation \: is \: \: \: {x}^{2} - \frac{7x}{2} + ( - \frac{5}{2} ) = 0 \\ \\ 2 {x}^{2} - 7x - 5 = 0.$