Question

if alpha and beta are zeros of polynomial 3 x square - 4 x minus 7 form a quadratic polynomial whose zeros are one by Alpha ,one by beta

Need. Good ans​

Answer 1

here's your solution bud!

Answer 2

Step-by-step explanation:

Hey mate,

Answer:-

We will campare

${3x}^{2} - 4x - 7$

With quadratic polynomial

Therefore

a=3

b=-4 and c=-7

$\alpha + \beta = \frac{ - b}{a} = \frac{ - ( - 4)}{3} = \frac{4}{3} \\ \alpha \beta = \frac{c}{a} = \frac{ - 7}{3}$

Bb we have to form quadratic equation

Therefore

Sum of zeros

$\frac{1}{ \alpha } + \frac{1}{ \beta } = \frac{ \beta + \alpha }{ \alpha \beta } \\ \\ nwow \: put \: above \: vaule \: \\ \: = - \frac{ - 4}{7} \\ product \: of \: zeroes \\ \frac{1}{ \alpha } \times \frac{1}{ \beta } \\ = \frac{1}{ \frac{ - 7}{3} } = \frac{3}{ - 7}$

We have formula

=

$= > k( {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes$

$k( {x}^{2} - ( - \frac{ - 4}{7} )x + \frac{ - 3}{7}$

If k=7 then

Required polynomial will be

${7x}^{2} + 4x - 3$