Question

find the zero of the quadratic polynomial X square + 5 x + 6 and verify the relationship between the zeros and the coefficients​

Answer 1

Question: Find the zero of the quadratic polynomial $x^{2}+5x+6$ and verify the relationship between the zeros and the coefficients​.

Solution:

◼We know that a polynomial with degree 2 is a quadratic polynomial.

◼A quadratic polynomial has 2 zeroes.

Step 1️⃣- Factorizing:

$x^{2}+5x+6$

$x^{2}+3x+2x+6$ (Splitting the middle term)

$x(x+3)+2(x+3)$

$(x+2)(x+3)$

Step 2️⃣- Finding zeroes:

$(x+2)$= 0

$x$= 0-2

$x$= -2

$(x+3)$= 0

$x$= 0-3

$x$= -3

Hence, the two zeroes(α and β) are -2 and -3.

Step 3️⃣- Verifying the relationship between the zeroes and the co-efficients:

In the equation, $a=1$;$b=5$  and $c=6$

Sum of the zeroes(α+β) = $\frac{-b}{a}$

$(-2)+(-3)$ = $\frac{-5}{1}$

$-2-3 = -5$

$-5 = -5$

LHS = RHS

Hence proved.

Product of the zeroes(αβ) = $\frac{c}{a}$

$(-2)(-3)$ = $\frac{6}{1}$

$6 = 6$

LHS = RHS

Hence proved.

Answer 2

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