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opudodennis

Answer:

Product is 2.25

Sum is -3.75

Step-by-step explanation:

The equayion

[tex]4x^{2}+15x+9=0[/tex]

Is solved as follows

By factorization

(4x+3)(x+3)=0

X+3=0 hence x=-3

4x+3=0 hence x=-3/4=-0.75

Product of -3 and -0.75 is -3*-0.75=2.25

Sum of -3 and -0.75=-3.75

The sum of the roots is -3.75 and product of the roots is 2.25

Given-

The given equation is,

[tex]4x^2+15x+9=0[/tex]

Use splitting of middle term on the above equation, we get,

[tex]4x^2+3x+12x+9=0[/tex]

[tex]x(4x+3)+3(4x+3)=0[/tex]

[tex](4x+3)(x+3)=0[/tex]

Equate the above equation with zero to find the roots, we get,

[tex]4x+3=0[/tex]

[tex]x=\dfrac{-3}{4}[/tex]

and,

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

Thus the roots of the equation is -3/4 and -3.

  • Sum of the roots is,

[tex]=\dfrac{-3}{4}+(-3)[/tex]

[tex]=-0.75-3=-3.75[/tex]

  • Product of the equation is,

[tex]=-0.75\times (-3)[/tex]

[tex]=2.25[/tex]

Hence, the sum of the roots is -3.75 and product of the roots is 2.25.

For more about the quadratic equation, follow the link below-

https://brainly.com/question/2263981

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