Question

slove : 5x²-3x-2=0.in mathematics class 10 section A​

Answer 1

Answer:

x = 1 & -2/5

Step-by-step explanation:

5x² - 3x - 2 = 0

5x² - 5x + 2x - 2 = 0

5x (x - 1) + 2 (x - 1) = 0

(5x + 2) (x - 1) = 0

x = 1 & -2/5

Answer 2

Answer:

The roots of the given quadratic equation are

$\displaystyle{\boxed{\red{\sf\:x\:=\:1\:}}\sf\quad\:OR\:\quad\:\boxed{\red{\sf\:x\:=\:-\:\dfrac{2}{5}\:}}}$

Step-by-step-explanation:

The given quadratic equation is 5x² - 3x - 2 = 0.

We have to find the roots of the given equation.

Comparing the given equation with ax² + bx + c = 0, we get,

5x² - 3x - 2 = 0

• a = 5
• b = - 3
• c = - 2

Now, by quadratic formula,

$\displaystyle{\boxed{\pink{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^2\:-\:4ac}}{2a}}}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{-\:(\:-\:3\:)\:\pm\:\sqrt{(\:-\:3\:)^2\:-\:4\:\times\:5\:\times\:(\:-\:2\:)}}{2\:\times\:5}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{3\:\pm\:\sqrt{9\:-\:(\:-\:40\:)}}{10}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{3\:\pm\:\sqrt{9\:+\:40}}{10}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{3\:\pm\:\sqrt{49}}{10}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{3\:\pm\:7}{10}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{3\:+\:7}{10}\:\quad\:OR\:\quad\:x\:=\:\dfrac{3\:-\:7}{10}}$

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{10}{10}}\:\quad\:OR\:\quad\:x\:=\:\dfrac{-\:\cancel{4}}{\cancel{10}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:1\:}}}\sf\quad\:OR\:\quad\:\underline{\boxed{\red{\sf\:x\:=\:-\:\dfrac{2}{5}\:}}}}$