Explain how to solve a^2 - 7a + c.

Question:

Explain how to solve {eq}a^{2} - 7a + c {/eq}.

Quadratic Formula:

Quadratic formula cane be used to solve any type of quadratic equation. For any Quadratic equation of the type {eq}ka^2+ba+m=0 {/eq}, the quadratic formula gives us the roots as ....

{eq}\displaystyle\alpha,\beta=\frac{-b\pm\sqrt{b^2-4km}}{2k} {/eq}

Answer and Explanation:

On comparing the quadratic equation given in the question with the standard form, we get that

{eq}k=1,b=-7,~\&~m=c {/eq}

Simply putting these values in the quadratic formula, we get {eq}\displaystyle\alpha,\beta=\frac{-(-7)\pm\sqrt{(-7)^2-4(1)(c)}}{2(1)}\\ \displaystyle\alpha,\beta=\frac{7\pm\sqrt{49-4c}}{2} {/eq}

So, this Quadratic equation will have two roots which are {eq}\displaystyle\alpha=\frac{7+\sqrt{49-4c}}{2}~\&~ \displaystyle\beta=\frac{7-\sqrt{49-4c}}{2} {/eq}


Learn more about this topic:

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The Quadratic Formula: Definition & Example

from Remedial Algebra I

Chapter 25 / Lesson 10
11K

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