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Find the roots of the quadratic equation by using the quadratic formula in the following: 2x2 – 3x – 5 = 0 - Mathematics

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प्रश्न

Find the roots of the quadratic equation by using the quadratic formula in the following:

2x2 – 3x – 5 = 0

बेरीज
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उत्तर

The quadratic formula for finding the roots of quadratic equation

ax2 + bx + c = 0, a ≠ 0 is given by,

x = `(-b +- sqrt(b^2 - 4ac))/(2a)`

∴ x = `(-(-3) +- sqrt(3^2 - 4(2)(-5)))/(2(2))`

= `(3 +- sqrt(49))/4`

= `(3 +- 7)/4`

= `5/2, -1`

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पाठ 4: Quadatric Euation - Exercise 4.3 [पृष्ठ ४०]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 10
पाठ 4 Quadatric Euation
Exercise 4.3 | Q 1.(i) | पृष्ठ ४०

संबंधित प्रश्‍न

Without solving, examine the nature of roots of the equation 2x2 + 2x + 3 = 0


Find the values of k for which the roots are real and equal in each of the following equation:

k2x2 - 2(2k - 1)x + 4 = 0


Find the values of k for which the given quadratic equation has real and distinct roots:

kx2 + 2x + 1 = 0


The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.


Discuss the nature of the roots of the following equation: `x^2 - (1)/(2)x - 4` = 0


Discuss the nature of the roots of the following equation: `5x^2 - 6sqrt(5)x + 9` = 0


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

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Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :

Solution :

Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0

a = 1, b = 2, c = `square`

∴ b2 – 4ac = (2)2 – 4 × `square` × `square`

Δ = 4 + `square` = 40

∴ b2 – 4ac > 0

∴ The roots of the equation are real and unequal.


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x2 + 4x – 8 = 0

Give your Solution correct to one decimal place.

(Use mathematical tables if necessary.)


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