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The two expressions below are equivalent. Find the values of a and b that make them equivalent.

The two expressions are:
5x^2+bx-12
(5x+a)(x-4)

Sagot :

XKelvinidn

Answer:

[tex]a=3\text{ and } b=-17[/tex]

Step-by-step explanation:

We are given that:

[tex]5x^2+bx-12=(5x+a)(x-4)[/tex]

First, we can distribute the right-hand side:

[tex]5x(x-4)+a(x-4)[/tex]

Distribute:

[tex]=5x^2-20x+ax-4a[/tex]

Rewrite:

[tex]=5x^2+(-20+a)x-(4a)[/tex]

Since it is equivalent to the above expression, the coefficients of the variables must match. This means that:

[tex]-20+a=b\text{ and } 12=4a[/tex]

Solving for a in the second equation gives:

[tex]a=3[/tex]

Therefore:

[tex]b=-20+3=-17[/tex]

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