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The given equation is x 2 +k(2x+k−1)+2=0. ⇒x 2 +2kx+k(k−1)+2=0 So, a = 1, b = 2k, c = k(k − 1) + 2 We know D=b 2 −4ac ⇒D=(2k) 2 −4×1×[k(k−1)+2] ⇒D=4k 2 −4[k2−k+2] ⇒D=4k 2 −4k2+4k−8 ⇒D=4k−8=4(k−2) For equal roots, D = 0 Thus, 4(k − 2) = 0 So, k = 2.

Subject

Mathematics

Class

CBSE Class 10

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CBSE Class 10 Mathematics Solved Question Paper 2017

Short Answer Type

The ratio of the height of a tower and the length of its shadow on the ground is √3:1. What is the angle of elevation of the sun?

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7.
Find the value of k for which the equation x² + k(2x + k − 1) + 2 = 0 has real and equal roots.

The given equation is x²+k(2x+k−1)+2=0.
⇒x²+2kx+k(k−1)+2=0
So, a = 1, b = 2k, c = k(k − 1) + 2
We know D=b²−4ac
⇒D=(2k)²−4×1×[k(k−1)+2]
⇒D=4k²−4[k2−k+2]
⇒D=4k²−4k2+4k−8
⇒D=4k−8=4(k−2)
For equal roots, D = 0
Thus, 4(k − 2) = 0
So, k = 2.

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Draw a line segment of length 8 cm and divide it internally in the ratio 4: 5.
Steps of construction.

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10.

A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1?

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