2.1 Quadratic Equations and Inequalities

Report 1 / 5

Solve the following quadratic equation by using completing the square method.

\(8x^2-9x-8=0.\)

(A)		\(\begin{aligned} x&=\dfrac{\sqrt{337}+9}{16}\\\\&\text{or} \\\\ &\dfrac{-\sqrt{337}-9}{16} \end{aligned}\)

(B)		\(\begin{aligned} x&=\dfrac{\sqrt{337}-9}{16}\\\\&\text{or} \\\\ &\dfrac{-\sqrt{337}-9}{16} \end{aligned}\)

(C)		\(\begin{aligned} x&=\dfrac{\sqrt{337}+9}{16}\\\\&\text{or} \\\\ &\dfrac{-\sqrt{337}+9}{16} \end{aligned}\)

(D)		\(\begin{aligned} x&=\dfrac{\sqrt{337}-9}{16}\\\\&\text{or} \\\\ &\dfrac{-\sqrt{337}+9}{16} \end{aligned}\)

Difficulty Level: Medium

Report 2 / 5

Form a quadratic equations from the following roots.

\(-\dfrac{3}{7}\) and \(-\dfrac{5}{8}\).

Difficulty Level: Medium

Report 3 / 5

Form a quadratic equations from the following roots.

\(\dfrac{2}{9}\) and \(\dfrac{6}{7}\).

Difficulty Level: Medium

Report 4 / 5

Find the range of the values of \(x\) which satisfy the following quadratic inequality.

\((x+3)(x-5)\leq0.\)

Difficulty Level: Medium

Report 5 / 5

Find the range of the values of \(x\) which satisfy the following quadratic inequality.

\(-x^2+5x+6\leq0.\)

Difficulty Level: Hard