Question
Solve for x using the quadratic formula. Write your answer correct to two significant figures $(x -1)^2 – 3x + 4 = 0.$
✓
Answer
$(x-1)^2-3 x+4=0$
$x^2+1-2 x-3 x+4=0$
$x^2-5 x+5=0$
Comparing it with
$a x^2+b x+c=0$, we get
$a = 1, b = -5, c = 5$
By using the formula,
$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a c}$
$=\frac{5 \pm \sqrt{25-20}}{2}$
$=\frac{5 \pm \sqrt{5}}{2}$
$x=\frac{5 \pm 2 \cdot 24}{2}$
$\text { Taking +ve sign } x=\frac{b+2 \cdot 24}{2} $
$ x=3.62$
Taking -ve sign $x=\frac{5-2 \cdot 25}{2}$
$=\frac{2 \cdot 76}{2}$
$=1.38$
Thus required value are $3.62$ and $1.38$
$x^2+1-2 x-3 x+4=0$
$x^2-5 x+5=0$
Comparing it with
$a x^2+b x+c=0$, we get
$a = 1, b = -5, c = 5$
By using the formula,
$x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a c}$
$=\frac{5 \pm \sqrt{25-20}}{2}$
$=\frac{5 \pm \sqrt{5}}{2}$
$x=\frac{5 \pm 2 \cdot 24}{2}$
$\text { Taking +ve sign } x=\frac{b+2 \cdot 24}{2} $
$ x=3.62$
Taking -ve sign $x=\frac{5-2 \cdot 25}{2}$
$=\frac{2 \cdot 76}{2}$
$=1.38$
Thus required value are $3.62$ and $1.38$
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