Question

One of the roots of 2x2-13x+20=0 is 4. What is the other root?
a.
$\frac{2}{5}$
b.
​

Answer 1

Answer:

x = 5/2

Step-by-step explanation:

2x^2 -13x+20=0

(2x-5)(x-4)=0

2x-5=0

x=5/2

x-4=0

x= 4

Answer 2

SOLUTION

GIVEN

One of the roots of 2x² - 13x + 20 = 0 is 4

TO DETERMINE

The other root

EVALUATION

Here the given equation is

2x² - 13x + 20 = 0

We now find the roots as below

$\displaystyle \sf{ 2 {x}^{2} - 13x + 20 = 0}$

$\displaystyle \sf{ \implies 2 {x}^{2} - (8 + 5)x + 20 = 0}$

$\displaystyle \sf{ \implies 2 {x}^{2} - 8 x - 5x + 20 = 0}$

$\displaystyle \sf{ \implies 2x(x - 4) - 5(x - 4) = 0}$

$\displaystyle \sf{ \implies (x - 4) (2x- 5) = 0}$

$\displaystyle \sf{ \implies x = 4 \: , \: \frac{5}{2} }$

Here it is given that one of its roots = 4

$\displaystyle \sf{ The \: other \: root = \frac{5}{2} }$

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