Question

Find a quadratic polynomial, the sum and product of whose zeros are 7/2 and −5/4

respectively.​

Answer 1

Answer:

$Quadratic \: polynomial = 8 {x}^{2} - 18x - 35$

Step-by-step explanation:

$α+β= \frac{7}{2} , \: αβ=\frac{( - 5)}{4} \\ </p><p>Quadratic \: polynomial \\ </p><p>=x²-(α+β)x+αβ \\ </p><p>=x²-{[ \frac{7}{2} + \frac{( - 5)}{4}]}x+( \frac{7}{2} )( \frac{( - 5)}{4} ) \\ </p><p>=x²-[ \frac{14 + ( - 5)}{4} ]x + \frac{( - 35)}{8} \\ = {x}^{2} - \frac{14 - 5}{4} x - \frac{35}{8} \\ = {x}^{2} - \frac{9}{4} x - \frac{35}{8} \\ multiply \: each \: term \: by \: 8 \\ = {x}^{2} \times 8 - \frac{9x}{4} \times 8 - \frac{35}{8} \times 8 \\ = 8 {x}^{2} - 9x \times 2 - 35 \\ = 8 {x}^{2} - 18x - 35$