Question

find the roots of
${x}^{2} - 3x - 10 = 0$
by 1. quadratic formula method 2. factorization method and 3. completing square method ​

Answer 1

✨HOLA✨

1.By quadratic formula method

D=b^2-4ac

$= ( - 3) {}^{2} - 4(1)( - 10)$

$= 9 + 40$

$= 49$

By quadratic formula,

x=((-b)± √D)/2a

x=((-3)±√49)/2 (1)

x=((-3)±7)/2

If x=((-3)-7)/2

x=(-10)/2

x=(-5)

If x=((-3)+7)/2

x=4/2

x=2

2.Factorisation Method

${x}^{2} - 3x - 10$

$= {x}^{2} - 5x + 2x - 10$

$= x(x - 5) + 2(x - 5)$

$= (x + 2)(x - 5)$

x=(-2),5

3. Completing square method

$x {}^{2} - 3x - 10 = 0$

$x {}^{2} - 3x = 10$

Adding ((1/2)× coefficient of x)^2 in both sides that is 9 by 4,

${x}^{2} - 3x + (9 \div 4) = 10 + (9 \div 4)$

${x}^{2} - (2 ( - 3 \div 2)x) + ( - 3 \div 2) {}^{2} = (40 + 9) \div 4$

$(x + (3 \div 2)) {}^{2} = 49 \div 4$

$x + (3 \div 2) = \sqrt{49 \div 4}$

x + (3 / 2) = ±(7 /2)

x=(3/2)±(7/2)

If x=(3/2)-(7/2)

x=(4/2)

x=2

If x=(3/2)+(7/2)

x=10/2

x=5

HOPE IT HELPS UHH #CHEERS