Question

(b) Solve: using factorisation method: x² – 3x - 10 = 0​

Answer 1

Step-by-step explanation:

Use the quadratic formula

=−±2−4√2

x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}x=2a−b±b2−4ac

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

2−3−10=0

x^{2}-3x-10=0x2−3x−10=0

=1

a={\color{#c92786}{1}}a=1

=−3

b={\color{#e8710a}{-3}}b=−3

=−10

c={\color{#129eaf}{-10}}c=−10

=−(−3)±(−3)2−4⋅1(−10)√2⋅1

x=\frac{-({\color{#e8710a}{-3}}) \pm \sqrt{({\color{#e8710a}{-3}})^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-10}})}}{2 \cdot {\color{#c92786}{1}}}x=2⋅1−(−3)±(−3)2−4⋅1(−10)

2

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Multiply the numbers

=3±72

x=\frac{3 \pm 7}{2}x=23±7

3

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

=3+72

x=\frac{3+7}{2}x=23+7

=3−72

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