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If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equation 4x²-2px k=0 has equal roots , find the value of k?
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If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equ...
Quadratic Equation 1: 3x² + ax - 2 = 0
Quadratic Equation 2: 4x² - 2px + k = 0
Given that 2 is a root of the first quadratic equation, we can substitute it into the equation to find the value of 'a'. When we substitute x = 2 into the equation 3x² + ax - 2 = 0, we get:
3(2)² + 2a - 2 = 0
12 + 2a - 2 = 0
2a + 10 = 0
2a = -10
a = -5
Now, let's consider the second quadratic equation, 4x² - 2px + k = 0. We are given that the equation has equal roots, which means that the discriminant of the equation must be equal to zero. The discriminant is given by:
Δ = b² - 4ac
In this case, a = 4, b = -2p, and c = k. Substituting these values into the discriminant equation, we have:
Δ = (-2p)² - 4(4)(k)
Δ = 4p² - 16k
Since the equation has equal roots, Δ = 0. Therefore, we can set the discriminant equal to zero and solve for 'k':
4p² - 16k = 0
4p² = 16k
p² = 4k
p = ±2√k
So, the value of 'k' is equal to p²/4.
Quadratic Equation 2: 4x² - 2px + k = 0
Given that 2 is a root of the first quadratic equation, we can substitute it into the equation to find the value of 'a'. When we substitute x = 2 into the equation 3x² + ax - 2 = 0, we get:
3(2)² + 2a - 2 = 0
12 + 2a - 2 = 0
2a + 10 = 0
2a = -10
a = -5
Now, let's consider the second quadratic equation, 4x² - 2px + k = 0. We are given that the equation has equal roots, which means that the discriminant of the equation must be equal to zero. The discriminant is given by:
Δ = b² - 4ac
In this case, a = 4, b = -2p, and c = k. Substituting these values into the discriminant equation, we have:
Δ = (-2p)² - 4(4)(k)
Δ = 4p² - 16k
Since the equation has equal roots, Δ = 0. Therefore, we can set the discriminant equal to zero and solve for 'k':
4p² - 16k = 0
4p² = 16k
p² = 4k
p = ±2√k
So, the value of 'k' is equal to p²/4.
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If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equ...
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If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equation 4x²-2px k=0 has equal roots , find the value of k?
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If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equation 4x²-2px k=0 has equal roots , find the value of k? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equation 4x²-2px k=0 has equal roots , find the value of k? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equation 4x²-2px k=0 has equal roots , find the value of k?.
If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equation 4x²-2px k=0 has equal roots , find the value of k? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equation 4x²-2px k=0 has equal roots , find the value of k? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2is root of the quadratic equation 3x²+ax-2=0 and the quadratic equation 4x²-2px k=0 has equal roots , find the value of k?.
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