find the roots of the equation by factrolization [tex]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 } [/tex] About the author Harper
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 Reply
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