If the quadratic equation has two roots, then find the value of

Subject

Mathematics

Class

CBSE Class 10

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 Multiple Choice QuestionsShort Answer Type

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1.

If the quadratic equation haspx squared minus 2 square root of 5px plus 15 equals 0 two roots, then find the value of p.


The given quadratic equation haspx squared minus 2 square root of 5px plus 15 equals 0 two equal roots.
therefore,

by using the discriminant method

straight b squared space minus space 4 ac space equals space 0 space.. left parenthesis straight i right parenthesis

straight b space equals space minus 2 square root of 5 straight p

straight a space space equals space straight p

straight c space equals space 15

thus comma space putting space the space value space in space equation space left parenthesis straight i right parenthesis
left parenthesis negative 2 square root of 5 straight p end root right parenthesis squared minus 4 space straight x space straight p space straight x 15 space equals 0

rightwards double arrow space left parenthesis negative 2 square root of 5 straight p right parenthesis squared minus 4 space straight x space straight p space straight x 15 space equals 0


⇒  20p2 - 60p = 0

⇒  20p (p - 3) = 0

⇒  p = 0 or p - 3 = 0

⇒  p = 0 or p = 3

p cannot be zero.

Hence, the value of p  is 3. 

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2.

In Given figure, a tower AB is 20 m high and BC, its shadow on the ground, is m20 square root of 3 long. Find the sun's altitude.

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3.

The different dice are tossed together. Find the probability that the product of the two number on the top of the dice is 6.

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4.

In the given figure, PQ is a chord of a circle with centre O and PT is tangent. If ∠QPT = 60o, find ∠ PRQ.

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5.

In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120o, then prove that OR = PR + RQ.

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6.

In the given figure, a triangle ABC is drawn to circumscribe of radius 3 cm, such that the segments RD and DC are respectively of length 6 cm and 9 cm. If the area of ΔABC is 54 cm2, then find lengths of sides AB and AC.

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7.

Solve the following quadratic equation for x,

4x2 + 4bx - (a2 - b2) = 0

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8.

In an AP, if S5 + S7 = 167 and S10 = 235, then find the AP,  Where Sn denotes the sum of its first n terms.

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9.

The points A (4, 7), B (p, 3) and C (7, 3) are the vertices a right triangle, right-angled at B find the value of p.

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10.

Find the relation between x and y if the points A (x, y), B (-5, 7) and C (-4, 5) are collinear.

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