Question

22. Find the quadratic polynomial whose zeroes are 1/4 and 1/8.​

Answer 1

$\huge{\bf{\underline{\underline{QuesTion:}}}}$

$Find \: the \: quadratic \: polynomial \\ \: whose \: zeroes \: \:are \: \frac{1}{4} \: and \: \frac{1}{8}.$

$\huge{\bf{\underline{\underline{AnsWer:}}}}$

$Sum \: of \: zeroes= \alpha + \beta \\ = = > \frac{1}{4} + \frac{1}{8} \\ ==> LCM \: of \: 4 \: and \: 8 \: is \: 8. \\ ==> \frac{1 \times 2}{4 \times 2} = \frac{2}{8} \\ ==> \frac{1 \times 1}{8 \times 1} = \frac{1}{8} \\ = = > \frac{2 + 1}{8} = \frac{3}{8}$

$Product \: of \: zeroes \: = \alpha \times \beta \\ = = > \frac{1}{4} \times \frac{1}{8} \\ = = > \frac{1}{32}$

Then, the quadratic polynomial

$= x² – (sum \: of \: zeroes)x + (product \: of \: zeroes) \\ x²-( \frac{3}{8} )x + \frac{1}{32}$

$= = > 32 {x}^{2} - 12x + 1$

Hope it helps !!

@SitaVeronica