Find the common root of equations 2x² + x – 6 = 0 and x² – 3x – 10 = 0.ORFind the sum of the roots of the quadratic equation -2x² + 7x + 9 = 0.
Answers
Answer:
Step-by-step explanation:
hey mate here is your answer:
1. 2x^2+x-6=0
2x^2+4x-3x-6=0
2x(x+2)-3(x+2)=0
(2x-3) (x+2)=0
x=+3/2,-2
2. x^-3x-10=0
x^2-5x+2x_10=0
x(x-5)+2(x-5)=0
(x+2) (x-5)=0
x=-2,+5
since ,common root in 2x^2+x-6=0 and x^-3x-10=0 is "-2".
3. sum of the roots of -2x^2+7x+9=0
.: sum of the roots =-b/a
-7/-2
7/2
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Answer:
The common root of equations 2x² + x – 6 = 0 and x² – 3x – 10 = 0 is (-2).
The sum of the roots of the quadratic equation -2x² + 7x + 9 = 0 is 3.5.
Explanation:
Given two equations are 2x²+x-6 = 0 and x² – 3x – 10 = 0.
Now, 2x²+x-6 = 0
2x²+(4-3)x-6 = 0
2x²+4x-3x-6 = 0
2x (x+2) -3 (x+2) = 0
(x+2) (2x-3) = 0
x = -2 of (3/2)
and x² – 3x – 10 = 0
x²-(5-2)x -10 = 0
x²-5x+2x-10 = 0
x(x-5)+2(x-5) = 0
(x-5)(x+2) = 0
x = 5 or (-2)
So,the common root of equations 2x² + x – 6 = 0 and x² – 3x – 10 = 0 is (-2)
Again we have the quadratic equation -2x² + 7x + 9 = 0.
We know if a quadratic equation ax²+bx+c = 0 has two roots p and q then sum of roots p+q = (-b/a)
We are comparing -2x² + 7x + 9 = 0 with ax²+bx+c = 0 then sum of roots = -(7/-2) = 3.5
This is a problem of Algebra.
Some important Algebra formulas.
(a + b)² = a² + 2ab + b²
(a − b)² = a² − 2ab − b²
(a + b)³ = a³ + 3a²b + 3ab² + b³
(a - b)³ = a³ - 3a²b + 3ab² - b³
a³ + b³ = (a + b)³ − 3ab(a + b)
a³ - b³ = (a -b)³ + 3ab(a - b)
a² − b² = (a + b)(a − b)
a² + b² = (a + b)² − 2ab
a² + b² = (a − b)² + 2ab
a³ − b³ = (a − b)(a² + ab + b²)
a³ + b³ = (a + b)(a² − ab + b²)
Know more about Algebra,
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2) https://brainly.in/question/1169549
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