Question

38) Find the zeroes of the quadraticPolynomial x² _ 7X + 12 and verify the relationship between the zeroes and the coefficients of the Polynomial .​

Answer 1

${\large{\pmb{\sf{\underline{Correct \; question...}}}}}$

★ Find the zeroes of the quadratic polynomial x²+7x+12 and verify the relationship between the zeroes and the coefficients of the polynomial .

${\large{\pmb{\sf{\underline{Given \; that...}}}}}$

★ The quadratic polynomial = x²+7x+12

${\large{\pmb{\sf{\underline{To \; determine...}}}}}$

★ The zeroes of the quadratic polynomial i.e., x²+7x+12

★ Verify the relationship between the zeroes and the coefficients of the polynomial.

${\large{\pmb{\sf{\underline{Solution...}}}}}$

★ The zeroes of the quadratic polynomial i.e., x²+7x+12 = -3 or -4

${\large{\pmb{\sf{\underline{Using \; concepts...}}}}}$

★ Sum of zeros of a quadratic polynomial is given by what?

★ Product of zeros of a quadratic polynomial is given by what?

${\large{\pmb{\sf{\underline{Using \; formulas...}}}}}$

★ Sum of zeros of a quadratic polynomial is given by -b/a

★ Product of zeros of a quadratic polynomial is given by c/a

${\large{\pmb{\sf{\underline{Here,}}}}}$

★ b is 7

★ a is 1

★ c is 12

${\large{\pmb{\sf{\underline{Full \; Solution...}}}}}$

~ Firstly let us find the zeroes of the quadratic polynomial.

↝ x²+7x+12

↝ x²+4x+3x+12

↝ x(x+4) + 3(x+4)

↝ (x+3) (x+4)

↝ x = -3 and x = -4

• Henceforth, -3 or -4 are the zeroes of the quadratic polynomial.

~ Now let's verify the relationship between the zeroes and the coefficients of the polynomial.

~ As we already know that the sum of zeros of a quadratic polynomial is given by -b/a. Henceforth,

↝ Sum of zeros = -b/a

↝ Sum of zeros = -7/1

↝ Sum of zeros = -7

~ Now as we already know that the product of zeros of a quadratic polynomial is given by c/a. Henceforth,

↝ Product of zeros = c/a

↝ Product of zeros = 12/1

↝ Product of zeros = 12

† Henceforth, verified!

${\large{\pmb{\sf{\underline{Additional \; knowledge...}}}}}$

Knowledge about Quadratic equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation