Question

find the zeros of x square +15x+54and verify the relationship between the zeros ​

Answer 1

Answer:

x² + 15x + 54

Step-by-step explanation:

x² +9x +6x+54 = 0

x(x+9)+6(x+9)=0

(x+9)+(x+6)

x+9=0. x+6=0

x=-9. x=-6

Answer 2

The zeros of the equation are $\alpha=-6$ and $\beta=-9$.

Step-by-step explanation:

Given : Equation $x^2+15x+54$

To find : The zeros of equation and verify the relationship between the zeros?

Solution :

Equation $x^2+15x+54=0$

Solve by middle term split,

$x^2+9x +6x+54 = 0$

$x(x+9)+6(x+9)=0$

$(x+9)+(x+6)$

$x+9=0,x+6=0$

$x=-9,-6$

The zeros of the equation are $\alpha=-6$ and $\beta=-9$.

On comparing quadratic equation, a=1, b=15 and c=54

The sum of the zeros is $\alpha+\beta =-\frac{b}{a}$

$-6+(-9)=-\frac{15}{1}$

$-15=-15$

Verified.

The product of the zeros is $\alpha\times \beta =\frac{c}{a}$

$-6\times(-9)=\frac{54}{1}$

$54=54$

Verified.

#Learn more

Solve X and Y 2x - y - 6 = 0. 2x - 5 - 2 = 0 ​

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