Question

. For the polynomial 2y²+7y+5, the value of α²+β² will be​

Answer 1

SOLUTION:-

2y² + 7y + 5 = 0

comparing this equation with general form of quadratic equation ax² + bx + c = 0.

we get

=> a = 2, b = 7 , c = 5

now,

$</p><p></p><p>\sf \small \: \:</p><p>\alpha + \beta = \frac{-b}{a} = \frac{7}{2} \\ \\</p><p></p><p>\sf \small \: \:</p><p>\alpha \beta = \frac{c}{a} = \frac{5}{2} \\ \\</p><p></p><p>\tt now, \\ \\</p><p></p><p>\sf \small \: \: </p><p></p><p>\alpha ^2 + \beta ^2 = (\alpha + \beta)^2 - 2 \alpha \beta \\ \\ </p><p></p><p>\sf \small \: \:</p><p>\therefore = (\frac{7}{2})^2 - 2 \times \frac{5}{2} \\ \\</p><p></p><p>\sf \small \: \:</p><p></p><p> = \frac {49}{4} - 5 \\ \\</p><p></p><p>= \frac{49 - 20}{20} = \frac {29}{20} \\ \\ \</p><p></p><p>\tt \small The \: value \: for \: \: \alpha ^2 + \beta ^2 = \\ </p><p></p><p> \tt \small \: \: \frac{29}{20}</p><p></p><p>$

Answer 2

Answer: - 1

Step-by-step explanation: