Solveeit Logo

Question

Question: If a, b are the roots of the equation 2x<sup>2</sup> – 3x – 5 = 0, then the equation whose roots are...

If a, b are the roots of the equation 2x2 – 3x – 5 = 0, then the equation whose roots are 5/a, 5/b is

A

x2 – 3x – 10 = 0

B

x2 + 3x – 10 = 0

C

x2 + 3x + 10 = 0

D

x2 – 3x + 10 = 0

Answer

x2 + 3x – 10 = 0

Explanation

Solution

5α5β\frac{\frac{5}{\alpha}}{\frac{5}{\beta}} = x

α5β5\frac{\frac{\alpha}{5}}{\frac{\beta}{5}} = 1x\frac{1}{x}

x = a/b = 5x\frac{5}{x}

Replace x ®5x\frac{5}{x}

Req. eqn. Ž 2(5x)22\left( \frac{5}{x} \right)^{2}3(5x)53\left( \frac{5}{x} \right)–5 = 0

x2 + 3x – 10 = 0