Question

find the quadratic polynomial whose zeroes are-

-4 and 3/2​

Answer 1

2x² + 5x - 12

Step-by-step explanation:

Given -

• Zeros of a quadratic polynomial => - 4 and 3/2 .

To find -

• The polynomial .

Solution -

Let α = -4 and β = 3/2.

We can form a αβuadratic equation whose roots are given by using the formula -

$p(x) = k( {x}^{2} -Sx +P)$

where , k = constant

S = sum of the roots

P = product of the roots

Now , S = α + β

→ S = -4 + 3/2

→ S = -5/2

P = αβ

→ P = -4 × 3/2

→ P = - 6

(Putting the values in the formula)

$→\large{p(x)} = \Large k[ {x}^{2} -( \frac{ - 5}{2}) x +( - 6)]$

$→\large{p(x)} = \Large{k( {x}^{2} + { \frac{ 5}{2}}x - 6)}$

$→ \large p(x) = \Large {k( \frac{2 {x}^{2} + 5x - 12}{2})}$

$→ \large p(x) = \large {2 {x}^{2} +5x - 12} \: \: \: (k = 2)$

Hence , the polynomial is 2x² + 5x - 12 .