Question

Find the roots of the following quadratic equations by factorisation: 2x^2-7x+6

Answer 1

$\mathfrak{hello \: friend \: here \: is \: your \: answer} \\ \sf \red{2 {x}^{2} - 7x + 6 = 0} \\ \sf \green{2 {x}^{2} - 4x - 3x + 6 = 0 } \\ \sf \green{2x(x - 2) - 3(x - 2) = 0} \\ \sf \green{(2x - 3)(x - 2) = 0} \\ \sf \green{(2x - 3) = 0 \: and \: (x - 2) = 0} \\ \sf \blue { \boxed{x = \frac{3}{2}or \: x = 2 }}$

Hope my answer will help you...

Answer 2

$\large\bf\underline{Given:-}$

• Quadratic equation :-2x² - 7x + 6

$\large\bf\underline {To \: find:-}$

• Roots of the given quadratic equation.

$\huge\bf\underline{Solution:-}$

Given Quadratic equation = 2x² - 7x + 6

↣ 2x² - 7x + 6

↣2x² - 4x - 3x + 6

↣ 2x (x - 2) -3(x - 2)

↣ (2x -3)(x-2)

↣ x = 3/2 or x = 2

▶️ Verification :-

Let α and β are the roots of the given quadratic equation.

• Let α = 3/2
• and β = 2

≫ 2x² - 7x + 6

a = 2

b = -7

c = 6

✥Sum of zeroes = -b/a

≫ α+ β = -(-7)/2

≫ 3/2 + 2 = 7/2

≫ (3 + 4)/2 = 7/2

≫ 7/2 = 7/2

✥ Product of zeroes = c/a

≫ αβ = 6/2

≫ 3/2 × 2 = 3

≫ 3 = 3

hence,

✝ LHS = RHS

so, roots of the given quadratic equation is correct.

▶️ Roots are = 3/2 and 2

$\rule{200}3$