If one root of the polynomial p(y) = 5y2 + 13y + m is reciprocal of other, then the value of m isa)6b)0c)5d)1/5Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Let the roots be α and 1/α.

Product of roots = α(1/α) = 1
⇒ m/5 = 1
⇒ m = 5

Answer

Let one root is x & other is 1/x
so x.1/x=m/5
so M=5

For opening last minute points to remember for Quadratic Equation:

Points to Remember: Quadratic Equations
https://edurev.in/studytube/points-to-remember-quadratic-equations/4ee4d05c-ea3f-4122-a40d-ef79c2f43e5e_p

Answer

Solution:
Given, one root of the polynomial p(y) = 5y^2 - 13y + m is reciprocal of the other.

Let the roots of the polynomial p(y) be α and β such that αβ = 1.

We know that the sum of the roots of the quadratic equation is given by -b/a and the product of the roots is given by c/a. Here, a = 5, b = -13 and c = m.

Sum of roots, α + β = -b/a = 13/5
Product of roots, αβ = 1

Now, we have two equations α + β = 13/5 and αβ = 1.

Solving the equations, we get α = 5 and β = 1/5.

Since α and β are the roots of the polynomial p(y), we can write p(y) as (y - α)(y - β).

p(y) = (y - 5)(y - 1/5)

Expanding the above expression, we get

p(y) = y^2 - (5 + 1/5)y + 5/5

p(y) = y^2 - (26/5)y + 1

Comparing this with the given polynomial p(y) = 5y^2 - 13y + m, we get

m = 5/1 = 5

Therefore, the value of m is 5.

Hence, option C is the correct answer.

Answer

Let the zero of Polynominal be alpha and 1/alpha
Polynominal of p(x) =5y^2+13y+m
products of zero= c/a
1/alpha X alpha =m/5
1=m/5
5 =m
m=5

Answer

Option c

Answer

5

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