Question

find the zeros of the quadratic polynomial(x2-5x+6) and verify the relation between the zeroes and the coefficients

Answer 1

x2-5x+6

x2+x-6x+6

x(x+1)-6(x+1)

(x-6)(x+1)

x=6. x=-1

Relationship between the zeroes

Sum=a+b= -b/a

=6-1=-(-5)/1

=5=5

Product=ab=c/a

=(6)(-1)=6

=6=6

Answer 2

The zeros of the quadratic equation are 2 and 3.

Step-by-step explanation:

Given : The quadratic polynomial $x^2-5x+6$.

To find : The zeros of the quadratic polynomial and verify the relation between the zeroes and the coefficients ?

Solution :

The quadratic polynomial $x^2-5x+6$.

Solve by middle term split,

$x^2-3x-2x+6=0$

$x(x-3)-2(x-3)=0$

$(x-3)(x-2)=0$

$x=3,x=2$

Let $\alpha=3$ and $\beta =2$

Here, a=1, b=-5 and c=6

Relationship between the zeroes  and the coefficients,

The sum of zeros is

$\alpha+\beta=-\frac{b}{a}$

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

$5=5$

The product of zeros is

$\alpha\beta=\frac{c}{a}$

$3\times 2=\frac{6}{1}$

$6=6$

Therefore, the zeros of the quadratic equation are 2 and 3.

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