Question

Find the zeroes of the quadratic polynomial x2 + 7x + 12, and verify the relation between the zeros
and its coefficients.

Answer 1

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

Answer 2

In algebra, a quadratic equation is any equation that can be rearranged in standard form as $ax^{2}+bx+c=0$ where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no $ax^2$ term.

$ax^2+bx+c=0$

Given that, zeros the quadratic polynomial is $x^2+ 7x + 12.$

Since the above equation is in the form $ax^2 + bx + c= 0.$

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

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

$\rightarrow x^2 + 7x + 12 = 0$

We have to split 7x in such a way that it's addition become 7x and on multiplying we get $12x^2$

$\rightarrow x^2 + 4x + 3x + 12 = 0$

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

$\rightarrow x^2 + 4x + 3x + 12 = 0$

Now, take the common

$\rightarrow x(x + 4) + 3(x + 4) = 0\\\rightarrow (x + 4) (x + 3) = 0$

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

$\rightarrow x = -4, -3$

So, zeros are -4 and -3.

We have quadratic polynomial $= x^2 + 7x + 12.$

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

$(-4) \times (-3) = 12/1\\12 = 12$

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