Question

find the quadratic polynomial whose zeros are -4 and 3/2​

Answer 1

Answer:

first

sum of root = -5/2

product=-6

the answer is x^2+5/2x-6=0

2x^2+5x-6=0

Answer 2

Quadratic polynomial is $\bf \red{{x}^{2} + \frac{5}{2} x - 6}$.

Given:

• Zeros of quadratic polynomial are -4 and 3/2.

To find:

• Find the quadratic polynomial.

Solution:

Concept to be used:

• If x= a is one of the zero of polynomial, then (x-a) is one of its factor.

Step 1:

One zero is -4.

So,

$x = - 4$

Thus,

$(x + 4)$ is one of the factor.

Step 2:

Second zero is 3/2.

So,

$x = \frac{3}{2}$

Thus,

$\left(x - \frac{3}{2}\right )$ is another factor.

Step 3:

Multiply both factors to find the polynomial.

So,

$(x + 4) \left(x - \frac{3}{2}\right)$

or

$\implies {x}^{2} - \frac{3}{2} x + 4x - 4 \times \frac{3}{2}$

or

$\implies {x}^{2} + ( \frac{8 - 3}{2}) x - 6$

or

$\implies \: \bf {x}^{2} + \frac{5}{2} x - 6$ is the quadratic polynomial.

Note*:

Quadratic equation can be written as

${x}^{2} + \frac{5}{2} x - 6 = 0$

or

$\bf 2 {x}^{2} + 5x - 12 = 0$

Thus,

Quadratic polynomial is $\bf {x}^{2} + \frac{5}{2} x - 6$.

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