Question

write the quadratic polynomial whose roots are -3 and 4​

Answer 1

Solution :-

As given

→ Roots of Quadratic equation = -3 and 4

As we know that any Quadratic equation is in the form of

→ ax² + bx + c

Where

-b/a = Sum of roots

c/a = Product of roots

Let us consider a as any constant 'k' , then :-

-b/k = sum of roots

c/k = product of roots

and equation = k( x² + b/k + c/k )

Now

b/k = - sum of roots

= -(-3 + 4)

= -(1)

= -1

c/k = product of roots

= (-3) × (4)

= -12

Now we will substitute the values :-

= k( x² - x - 12)

So Quadratic equation

= k( x² - x - 12)

or when k = 1

= x² - x - 12

Answer 2

Answer:

x² - x - 12

Step-by-step explanation:

Given that-

Roots of quadratic polynomial are (-3) and 4. Let us consider, the roots of the equation be α and β. Thus,

α = -3 and β = 4,

Now, find the value of (α + β) -

(α + β) = - 3 + 4

= 1

Find the value of (αβ) -

(αβ) = (-3) * 4

= - 12

We know that -

Quadratic polynomial is given by -

= x² - (α + β)x + αβ

= x² - 1x + (-12)

= x² - x - 12

Hence, the required polynomial is x² - x - 12.