# How do you find the zeros of the function f(x)=(20x^2+11x−40)/(2x+5)?

Camila Brandt 2022-09-26 Answered
How do you find the zeros of the function $f\left(x\right)=\frac{20{x}^{2}+11x-40}{2x+5}$?
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Simeon Hester
the denominator of f(x) cannot be zero as this would make f(x) undefined
the zeros are found by equating the numerator to zero
$⇒\text{solve}\phantom{\rule{1ex}{0ex}}20{x}^{2}+11x-40=0←\text{standard form}$
solve using the quadratic formula
with a=20,b=11 and c=−40
$•xx=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$
$⇒x=\frac{-11±\sqrt{121+3200}}{40}$
$⇒x=\frac{-11±\sqrt{3321}}{40}=\frac{-11±9\sqrt{41}}{40}$
$⇒x=-\frac{11}{40}±\frac{9\sqrt{41}}{40}$
$⇒x=-\frac{11}{40}-\frac{9\sqrt{41}}{40}\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}x=-\frac{11}{40}+\frac{9\sqrt{41}}{40}$
$⇒\text{zeros are}\phantom{\rule{1ex}{0ex}}x\approx -1.72,x\approx 1.17\phantom{\rule{1ex}{0ex}}\text{to 2 dec. places}$