Question

find the roots of the equation by factrolization
$1.x { }^{2} - 3x - 10 = 0 \\2.2x {}^{2} +x - 6 = 0 \\ 3.100x {}^{2} - 20x + 1 = 0 \\ 4. \sqrt{2x {}^{2} } + 7x + 5 \sqrt{2 = 0 }$


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Answer 1

1. x²-3x-10=0

x²-5x+2x-10=0 product:- -10

x(x-5)+2(x-5)=0 sum:- -3

(x-5)(x+2)=0 no. :- -5,+2

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

x=5 or x=-2

the roots of quadratic equation is 5 and -2.

2. 2x²+x-6=0

2x²+4x-3x-6=0 product:- -6×2 =-12

2x(x+2) -3(x+2)=0 sum:- 1

(x+2)(2x-3)=0 no. :- +4, -3

(x+2)=0 or (2x-3)=0

x=-2 or 2x=3

x=-2 or x=3/2

the roots of quadratic equation is -2 and 3/2.

3. 100x²-20x+1=0

100x²-10x-10x+1=0. pro.-100×1=100

10x(x-10)-1(x-10)=0

(x-10)(x-10)=0

(x-10)=0 or (x-10)=0

x=10 or x=10

the roots of quadratic equation is 10.

4.√2x²+7x+5√2=0

√2x² +5x+2x+5√2 = 0

x(√2x + 5) +√2(√2x+5)=0

(√2x+5)(x + √2) = 0

x + √2=0 or √2x+5=0

x=-√2 or √2x=-5

x=-√2 or x=-5/√2

the roots of quadratic equation is -√2 or -5/√2