Question

find the zeroes of the quadratic polynimial x^2+7x+12 and verify the relationship between the zeroes and its coefficient​

Answer 1

Answer:

Here you go

Step-by-step explanation:

Given that, zeros the quadratic polynomial is x² + 7x + 12.

Since the above equation is in the form ax² + bx + c= 0.

So, we can solve it by Quadratic formula or by Splitting the middle term.

Now, let's solve it by splitting the middle term.

→ x² + 7x + 12 = 0

We have to split 7x in such a way that it's addition become 7x and on multiplying we get 12x²

→ x² + 4x + 3x + 12 = 0

Here, addition of 4x and 3x is 7x & Multiplication of 4x and 3x is 12 x²., which is correct.

→ x² + 4x + 3x + 12 = 0

Now, take the common

→ x(x + 4) + 3(x + 4) = 0

→ (x + 4) (x + 3) = 0

As, both (x+4)(x+3) are equal to 0. So,

→ x = -4, -3

So, zeros are -4 and -3.

We have quadratic polynomial = x² + 7x + 12.

Here, a = 1, b = 7 and c = 12

Now,

Sum of zeros = -b/a

-4 + (-3) = -7/1

-4 - 3 = -7

-7 = -7

Product of zeros = c/a

(-4) × (-3) = 12/1

12 = 12

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Answer 2

Step-by-step explanation:

there fore x=-4 or -3

by substitution the polynomial equation satisfies.