Question

Use division algorithm to find all the zeroes of the polynomial p(x) = 6x4
-10x3
-
25x2+35x+14, if two of its zeroes are √
଻
ଶ
and - √
଻
ଶ
.

Answer 1

square roots

quadratic equations like x^2=36 or (x-2)^2=49.

Square roots

Special products of binomials

What you will learn in this lesson

So far you have solved linear equations, which include constant terms—plain numbers—and terms with the variable raised to the first power, x^1=xx

1

=xx, start superscript, 1, end superscript, equals, x.

You will now learn how to solve quadratic equations, which include terms where the variable is raised to the second power, x^2x

2

x, squared.

Here are a few examples of the types of quadratic equations you will learn to solve:

x^2=36x

2

=36x, squared, equals, 36

(x-2)^2=49(x−2)

2

=49left parenthesis, x, minus, 2, right parenthesis, squared, equals, 49 Why is this a quadratic equation?

x^2

x, squared(x-2)^2

left parenthesis, x, minus, 2, right parenthesis, squaredxx

\begin{aligned}(x-2)^2&=49\\\\ x^2-4x+4&=49\end{aligned}

x^2

x, squared

2x^2+3=1312x

2

+3=131

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