Question

if a and B are the zeros of the quadratic polynomial f(x) = x squre 2 +3x-10 ,then find a quadratic polynomial whose zeros are 1/2a+B and 1/2B+a

Answer 1

please write the question clearly. it the question is 2x^2+3x-10

Answer 2

${x}^{2} + 3x - 10 = 0 \\ {x}^{2} + 5x - 2x - 10 = 0 \\ x(x + 5) - 2(x + 5) = 0 \\ (x + 5)(x - 2) = 0 \\ x = - 5 \\ x = 2$
A= -5
B= 2
now calculate zeros of other polynomial
$\frac{1}{2}a + b = \frac{1}{2} ( - 5) + 2 = \frac{ - 5 + 4}{2} = \frac{ - 1}{2}$
$\frac{1}{2} b + a = \frac{1}{2} \times 2 + - 5 = - 4$
one zero is -1/2 and other is -4
$\frac{ - b}{a} = - \frac{1}{2} - 4 = \frac{ - 9}{2} \\ \frac{c}{a} = ( \frac{ - 1}{2} )( - 4) = 2$
put the values
${x}^{2} - ( \frac{ - b}{a} )x + \frac{c}{a} = 0 \\ {x}^{2} - ( \frac{ - 9}{2} )x + 2 = 0 \\ 2 {x}^{2} + 9x + 4 = 0$
is the required polynomial