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Standard X

Mathematics

Nature of Roots

If the equati...

Question

If the equation $x^{2} - m (2 x - 8) - 15 = 0$ has equal roots, then $m =$

3, - 5

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- 3, 5

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3, 5

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- 3, - 5

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Solution

The correct option is D $3, 5$
The equation $x^{2} - m (2 x - 8) - 15 = 0$ has equal roots.
$\Rightarrow x^{2} - 2 m x + 8 m - 15 = 0$
Applying the condition for equal roots
i.e $D = b^{2} - 4 a c = 0$
$\Rightarrow 4 m^{2} = 4 (8 m - 15)$
$\Rightarrow 4 m^{2} - 32 m + 60 = 0$
$\Rightarrow m^{2} - 8 m + 15 = 0 \Rightarrow (m - 3) (m - 5) = 0$
$∴ m = 3$ or $m = 5$
Hence, option C is correct

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Similar questions

Q. If the roots of the equation

x^{2} - 15 - m (2 x - 8) = 0

are equal, then

m =

Q. The set of all values of m for which both the roots of the equation

x^{2} - (m + 1) x + m + 4 = 0

are real and negative, is
(a)

(- \infty, - 3] \cup [5, \infty)

(b) [−3, 5]
(c) (−4, −3]
(d) (−3, −1]

Q. The roots of the equation

\frac{3}{x - 5} + \frac{2 x}{x - 3} = 5

are (where

x \neq 3, 5

)

Q. Find the values of

m

for which the quadrilateral equation

x^{2} - m (2 x - 8) - 15 = 0

has
(i) equal roots
(ii) both roots positive.

Q. Choose the correct answers for the following questions.
(1) Which one is the quadratic equation ?

(A)

\frac{5}{x} - 3 = x^{2}

(B) x(x + 5) = 2

(D)

\frac{1}{x^{2}} (x + 2) = x

(2) Out of the following equations which one is not a quadratic equation ?

(A) x² + 4x = 11 + x²

(B) x² = 4x

(D) 2x – x² = x² + 5

(3) The roots of x² + kx + k = 0 are real and equal, find k.

\sqrt{2} x^{2} - 5 x + \sqrt{2} = 0

find the value of the discriminant.

(A) –5

(B) 17

(C)

\sqrt{2}

(D)

2 \sqrt{2} - 5

(5) Which of the following quadratic equations has roots 3,5 ?

(A) x² – 15x + 8 = 0	(B) x² – 8x + 15 = 0
(C) x² + 3x + 5 = 0	(D) x² + 8x – 15 = 0

(6) Out of the following equations, find the equation having the sum of its roots –5.

(A) 3x² – 15x + 3 = 0	(B) x² – 5x + 3 = 0
(C) x² + 3x – 5 = 0	(D) 3x² + 15x + 3 = 0

(7)

\sqrt{5} m^{2} - \sqrt{5} m + \sqrt{5} = 0

which of the following statement is true for this given equation ?

(A) Real and uneual roots	(B) Real and equal roots
(C) Roots are not real	(D) Three roots.

(8) One of the roots of equation x² + mx – 5 = 0 is 2; find m.

(A) –2

(B)

- \frac{1}{2}

(C)

\frac{1}{2}

(D) 2

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If the equation x2−m(2x−8)−15=0 has equal roots, then m=

The correct option is D 3,5The equation x2−m(2x−8)−15=0 has equal roots.⇒x2−2mx+8m−15=0Applying the condition for equal rootsi.e D=b2−4ac=0⇒4m2=4(8m−15)⇒4m2−32m+60=0⇒m2−8m+15=0⇒(m−3)(m−5)=0∴m=3 or m=5Hence, option C is correct

If the equation $x^{2} - m (2 x - 8) - 15 = 0$ has equal roots, then $m =$