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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

If the Roots of 2x2 - 6x + K = 0 Are Real and Equal, Find K. - Algebra

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प्रश्न

If the roots of 2x2 - 6x + k = 0 are real and equal, find k.

उत्तर

The roots of the quadratic equation are real and equal.
   ∴ b² - 4ac = 0
     (-6)² - 4 × 2 × k = 0
                       - 8k = -36
                           `k = 9/2`

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2018-2019 (March) Balbharati Model Question Paper Set 1

संबंधित प्रश्‍न

If α and β are the roots of the quadratice equation x²- 2x - 7= 0, find the
value α² + β²


If one root of the quadratic, x2 - 7x + k = 0 is 4. then find the value of k.


Form the quadratic equation if its roots are 5 and 7. 


Choose the correct alternative answer for the following sub questions and write the correct alphabet.

Degree of quadratic equation is always ______


If one of the roots of quadratic equation x2 + kx + 54 = 0 is – 6, then complete the following activity to find the value of ‘k’.

Activity: One of the roots of the quadratic equation x2 + kx + 54 = 0 is – 6.

Therefore let’s take x = ______

(– 6)2 + k(– 6) + 54 = 0

(______) – 6k + 54 = 0

– 6k + ______ = 0

k = ______


If one of the roots of quadratic equation x2 – kx – 15 = 0 is – 3, then find the value of ‘k’


If the roots of the given quadratic equation are real and equal, then find the value of ‘k’

kx(x – 2) + 6 = 0


Solve the following quadratic equation.

`sqrt(3) x^2 + sqrt(2)x - 2sqrt(3)` = 0


Determine whether 2 is a root of quadratic equation 2m2 – 5m = 0.


One of the roots of equation kx2 – 10x + 3 = 0 is 3. Complete the following activity to find the value of k.

Activity:

One of the roots of equation kx2 – 10x + 3 = 0 is 3.

Putting x = `square` in the above equation

∴ `"k"(square)^2 - 10 xx square + 3` = 0

∴ `square` – 30 + 3 = 0

∴ 9k = `square`

∴ k = `square`


Solve the following quadratic equation using formula:

x2 + 10x + 2 = 0


If the sum of the roots of the quadratic equation x2 + kx + 6 = 0 is 6, then the value of k is ______.


The value of the discriminant of the equation x2 + 6x – 15 = 0 is ______.


Is (x – 5) a factor of the polynomial x3 – 5x – 30?


One of the roots of equation x2 + 5x + a = 0 is – 3. To find the value of a, fill in the boxes.

Since, `square` is a root of equation x2 + 5x + a = 0

∴ Put x = `square` in the equation

⇒ `square^2 + 5 xx square + a` = 0

⇒ `square + square + a` = 0

⇒ `square + a` = 0

⇒ a = `square`


Find the roots of the quadratic equation `x^2 - (sqrt(3) + 1)x + sqrt(3)` = 0.


If 3 is one of the roots of the quadratic equation kx2 − 7x + 12 = 0, then k = ______.


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