Question

roots of 5x^2-7x+k=0 are sinA and CosecA then find the value of k​

Answer 1

Given :-

• Roots of 5x^2-7x+k=0 are sinA and CosecA ..

To Find :-

• Value of k ?

Concept used :-

The sum of the roots of the Equation ax² + bx + c = 0 , is given by = (-b/a)

and ,

→ Product of roots of the Equation is given by = c/a.

Solution :-

comparing The given Equation 5x² - 7x + k = 0 with ax² + bx + c = 0 we get ,

→ a = 5

→ b = (-7)

→ c = k

As, Product of Roots is given by (c/a), and we have given both roots are sinA & cosecA .

So,

→ Product of Roots = c/a

→ sinA * cosecA = k/5

→ sinA * (1/sinA) = k/5

→ 1 = k/5

→ k = 5 (Ans).

Hence, value of k will be 5.

Answer 2

____________________________

$\huge \tt {GIVEN:}$

• roots of 5x^2-7x+k=0 are sinA and CosecA

____________________________

$\huge \tt {SOLUTION:}$

Comparing the equations,

• a = 5
• b= (-7)
• c = k

Products of roots = c/a

Hence,

↪sinA× cosecA = k/5

↪sinA × (1/sinA) = k/5

↪1 = k/5

↪k = 5

Therefore,

$\tt {Value~Of~K=5}$

___________________________