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If the sum of the roots of the equation kx2 + 2x + 3k = 0 is equal to their product, then the value of k is: 1/3
-1/3
2/3
-2/3

Nội dung chính

    If the sum of the roots of the equation kx2 + 2x + 3k = 0 is equal to their product, then the value of k is: 
    Answer (Detailed Solution Below)
    Related Videos
    Is the product of zeros of the quadratic polynomial x Square 4 x K is 3 Find the value of K?
    What is the value of k in the quadratic polynomial K Square 4 x 3 K if the sum of the zeros is equal to their product?
    Is the product of the zeros of the polynomial x Square 6 x minus 6 is 4 find the value of a?
    How do you find a quadratic polynomial whose zeroes are given?

Answer (Detailed Solution Below)

Option 4 : -2/3

Free

Electric charges and coulomb’s law (Basic)

10 Questions 10 Marks

10 Mins

Given:

Given equation is kx2 + 2x + 3k = 0.

Sum of roots of the question = Product of roots of the question

Formula Used:

For a given quadratic equation ax2 + bx + c = 0,

The sum of the roots = -b/a

The product of the roots = c/a

Calculation:

According to the question,

given quadratic equation is kx2 + 2x + 3k = 0.

Comparing the given equation with the standard form of the quadratic equation ax2 +

bx + c = 0 we get,

a = k, b = 2 and c = 3k.

So, Sum of roots of the equation

⇒ -b/a

⇒ -2/k

and, Product of roots of the question

⇒ c/a

⇒ 3k/k

⇒ 3

Again, According to the question,

Sum of roots of the question = Product of roots of the question

⇒ -2/k = 3

⇒ k = -2/3

∴ The value of k = -2/3.

Key Points

Sum of roots = -b/ a

Product of roots = c/ a

Subtraction of roots = √D/a

where equation is ax2 + bx + c and D = (b2 – 4ac)

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Answer : 3

Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

105881768

0

8.5 K

2:21

यदि द्विघात बहुपद ` f (x) = x ^ 2 – 4x + k ` के शुन्यकों का गुणनफल 3 है तो ‘k’ का मान ज्ञात कीजिए |

1409560

0

5.0 K

0:37

If the product of zeros of the quadratic polynomial `f(x)=x^2-4x+k` is 3, find the value of `k` .

642568777

0

6.2 K

1:55

If the product of zeros of the quadratic polynomial `f(x)=x^2-4x+k` is 3, find the value of `k` .

75123

0

5.3 K

0:49

If the product of the zeros of a quadratic polynomial are `f(x)=x^2-4x+k` is 3 . find the value

473224151

0

9.3 K

1:20

यदि `p..(x) = x^3 – 2x^2 +4x +k` बहुपद का एक शून्यक x=1 हो, तो k का मान ज्ञात करें |

34839

0

3.7 K

4:54

Find the zeroes of the quadratic polynomial `x^2 -4x+ 3`. Find the zeroes of the quadratic polynomial `x^2+7x+10`.

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Is the product of zeros of the quadratic polynomial x Square 4 x K is 3 Find the value of K?

Solution : Product of the zero = `(“constant term”)/(“coefficient of ” x^(2)) = k/1. ` So, k = 3. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

What is the value of k in the quadratic polynomial K Square 4 x 3 K if the sum of the zeros is equal to their product?

Given that Sum of the zeroes is equal to their product. ⇒ k = -2/3. Therefore, the value of k = -2/3.

Is the product of the zeros of the polynomial x Square 6 x minus 6 is 4 find the value of a?

So a =4−6=2−3.

How do you find a quadratic polynomial whose zeroes are given?

Let the zeroes of the quadratic polynomial be α=3,β=−3 Then.. a+β=3+(−3)=0.. αβ=3×(−3)=−9.. Sum of zeroes =a+β=0.. Product of zeroes =αβ=−9.. Then, the quadratic polynomial =x2−( sum of zeroes )x+ product of zeroes =x2−(0)x+(−9). =x2−9..

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