Question

2x²-7x+6=0;x=3/2,+2,-3/2​

Answer 1

Step-by-step explanation:

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Answer 2

ANSWER:

Given:

• f(x) = 2x² - 7x + 6

To Find:

• f(3/2)
• f(2)
• f(-3/2)

Solution:

We are given that,

$\implies\rm{f(x)=2x^2-7x+6}$

We need to find the value of f(3/2), f(2) and f(-3/2).

So, we'll put the value of x as 3/2, 2 and -3/2 in respective case and find the answer.

1. x = 3/2

$\implies\rm{f(x)=2x^2-7x+6}$

$\implies\rm{f\left(\dfrac{3}{2}\right)=2\left(\dfrac{3}{2}\right)^2-7\left(\dfrac{3}{2}\right)+6}$

$\implies\rm{f\left(\dfrac{3}{2}\right)=2\!\!\!/\left(\dfrac{9}{4\!\!\!/_2}\right)-7\left(\dfrac{3}{2}\right)+6}$

$\implies\rm{f\left(\dfrac{3}{2}\right)=\dfrac{9}{2}-\dfrac{21}{2}+6}$

$\implies\rm{f\left(\dfrac{3}{2}\right)=\dfrac{9-21}{2}+6}$

$\implies\rm{f\left(\dfrac{3}{2}\right)=\dfrac{-12\!\!\!\!\!/^{\:\:6}}{2\!\!\!/}+6}$

$\implies\rm{f\left(\dfrac{3}{2}\right)=-6+6}$

$\implies\bf{f\left(\dfrac{3}{2}\right)=0}$

2. x = 2

$\implies\rm{f(x)=2x^2-7x+6}$

$\implies\rm{f(2)=2(2)^2-7(2)+6}$

$\implies\rm{f(2)=2(4)-7(2)+6}$

$\implies\rm{f(2)=8-14+6}$

$\implies\rm{f(2)=14-14}$

$\implies\bf{f(2)=0}$

3. x = -3/2

$\implies\rm{f(x)=2x^2-7x+6}$

$\implies\rm{f\left(\dfrac{-3}{2}\right)=2\left(\dfrac{-3}{2}\right)^2-7\left(\dfrac{-3}{2}\right)+6}$

$\implies\rm{f\left(\dfrac{-3}{2}\right)=2\!\!\!/\left(\dfrac{9}{4\!\!\!/_2}\right)-7\left(\dfrac{-3}{2}\right)+6}$

$\implies\rm{f\left(\dfrac{-3}{2}\right)=\dfrac{9}{2}+\dfrac{21}{2}+6}$

$\implies\rm{f\left(\dfrac{-3}{2}\right)=\dfrac{9+21}{2}+6}$

$\implies\rm{f\left(\dfrac{-3}{2}\right)=\dfrac{30\!\!\!\!\!/^{\:\:15}}{2\!\!\!/}+6}$

$\implies\rm{f\left(\dfrac{-3}{2}\right)=15+6}$

$\implies\bf{f\left(\dfrac{-3}{2}\right)=21}$