Question

3) Find a quadratic polynomial, the sum & product
of whose Zeroes
are -3/2 and -1 respectively?
​

Answer 1

Answer:

$sum \: of \: zeroes \: = \frac{ -3 }{2} - 1 = \frac{ - 5}{2} \\ product \: of \: zeroes \: = \frac{ - 3}{2} \times ( - 1) = \frac{3}{2} \\ so \: required \: quadratic \: polynomial \: is \\ p(x) = k( {x}^{2} - \frac{( - 5)}{2} x + \frac{3}{2} ) where \: k \: is \: non \: zero \: real \: number$

Answer 2

x² + 3x + 2
= x² + 2x + x + 2 = 0
= x(x+ 2) + 1 ( x + 2 ) = 0
= ( x+1 ) ( x + 2 ) = 0
= x = -1 , -2


α + ß = -3
α ß = 2


QUADRATIC POLYNOMIAL

= x² - ( α + ß )x + α ß
= x² - (-3)x + 2
= x² + 3x + 2