Question

(2) If the roots of the quadratic equation hx2 + 21x + 10 = 0, where h = 0, are in the ratio 2.5
find the possible values of h.​

Answer 1

Step-by-step explanation:

Given If the roots of the quadratic equation hx2 + 21x + 10 = 0, where h = 0, are in the ratio 2.5  find the possible values of h.

• The roots of the equation are in the ratio 2:5. Now the given equation is hx^2 + 21x + 10 = 0
• Now a = h, b = 21, c = 10
• Therefore sum of the roots = -b/a
•                                          = - 21 / h
•   So 2α + 5α = - 21 / h
•  So 7α = - 21 / h
•  So α = - 3 / h
•  Or h = - 3 / α-----------1
• So product of roots = c / a
•                                = 10 / h
• So (2α)(5α) = 10 / h
• Now 10 α^2 = 10 / h
• Or h = 1 / α^2 ------------------2
• Comparing 1 and 2 we get
• -3 / α = 1 / α^2
• So 1 / α = - 3
• Or α = - 1 / 3
• Now substituting in equation 1 we get
• So h = - 3 / - 1/3
• Or h = 9

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Answer 2

h = 9.

Explanation:-

Given Data:-

Equation hx^2 + 21x + 10 = 0, where h = 0,  

ratio 2:5  

h = ?

Sol:-

a = h, b = 21, c = 10

Sum of the roots = -b/a

                          = - 21 / h

2a + 5a = - 21 / h

7a= - 21 / h

a = - 3 / h

h = - 3 / a----------------1

Product of roots = c / a

                         = 10 / h

(2a)(5a) = 10 / h

10 a^2 = 10 / h

h = 1 / a^2 ------------------2

Comparing 1 and 2 we get

-3 / a = 1 / a^2

1 / a = - 3

a = - 1 / 3

Now substituting in equation 1

h = - 3 / (- 1/3).

h = 9.