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Chapter overview
Learning goals
Learning Goals
Maths
Summary
A quadratic equation in the form $ax^2+bx+c=0$ can be solved using the quadratic formula. Sometimes, it is necessary to use the quadratic formula to solve a quadratic rather than factorising, as not all quadratics can be factorised easily.
The quadratic formula is
$x= \dfrac{-b \pm \sqrt{b^2-4ac}} {2a}$
Where $a,b$ and $c$ are the co-efficients from the quadratic equation in the form
$ax^2+bx+c=0$
Substitute the values of $a, b$ and $c$ from the quadratic equation into the quadratic formula, and calculate the solutions for $x$.
Use the quadratic formula to solve
$2x^2+7x+3=0$
From the quadratic equation, $a=2, b=7$ and $c=3$. Substitute the numbers into the quadratic formula.
$x= \dfrac{-b \pm \sqrt{b^2-4ac}} {2a}$
$x= \dfrac {-7 \pm \sqrt {7^2-4\times2\times3}} {2 \times 2}\\$
Work out the value inside the square root.
$x= \dfrac {-7 \pm \sqrt {25}} {4}$
$x= \dfrac {-7 \pm 5} {4}\\$
The $\pm$ symbol means you have to do plus or minus, so there will be two calculations
$x = \dfrac {-7+5} 4 \space or \space x= \dfrac {-7-5} 4$
Therefore, the answers are
$\underline{x=-\frac 1 2} \space or \space \underline{x=-3}$
A quadratic equation in the form $ax^2+bx+c=0$ can be solved using the quadratic formula. Sometimes, it is necessary to use the quadratic formula to solve a quadratic rather than factorising, as not all quadratics can be factorised easily.
The quadratic formula is
$x= \dfrac{-b \pm \sqrt{b^2-4ac}} {2a}$
Where $a,b$ and $c$ are the co-efficients from the quadratic equation in the form
$ax^2+bx+c=0$
Substitute the values of $a, b$ and $c$ from the quadratic equation into the quadratic formula, and calculate the solutions for $x$.
Use the quadratic formula to solve
$2x^2+7x+3=0$
From the quadratic equation, $a=2, b=7$ and $c=3$. Substitute the numbers into the quadratic formula.
$x= \dfrac{-b \pm \sqrt{b^2-4ac}} {2a}$
$x= \dfrac {-7 \pm \sqrt {7^2-4\times2\times3}} {2 \times 2}\\$
Work out the value inside the square root.
$x= \dfrac {-7 \pm \sqrt {25}} {4}$
$x= \dfrac {-7 \pm 5} {4}\\$
The $\pm$ symbol means you have to do plus or minus, so there will be two calculations
$x = \dfrac {-7+5} 4 \space or \space x= \dfrac {-7-5} 4$
Therefore, the answers are
$\underline{x=-\frac 1 2} \space or \space \underline{x=-3}$
Factorising quadratics
FAQs
Question: What are the different ways to solve a quadratic?
Answer: A quadratic equation can be solved by factorising, using the quadratic formula or using complete the square.
Question: What is the quadratic formula used for?
Answer: The quadratic formula calculates the roots or solutions to a quadratic equation. The formula can be used as an alternative to factorising.
Question: When do you use the quadratic formula to solve a quadratic?
Answer: Sometimes, it is necessary to use the quadratic formula to solve a quadratic rather than factorising, as not all quadratics can be factorised easily.
Theory
Exercises
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