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Standard XII

Mathematics

Methods of Solving a Quadratic Equation

Which of the ...

Question

Which of the following is/are the roots of the quadratic equation,
$x^{2} - 8 x + 7 = 0$ ?

x = - 7

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x = - 1

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x = 1

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x = 7

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Solution

The correct option is D $x = 7$
Given,
$x^{2} - 8 x + 7 = 0$
Using completing the square method we can write,
$x^{2} - 2 (x) (\frac{8}{2}) + (\frac{8}{2})^{2} + 7 - (\frac{8}{2})^{2} = 0$
$\Rightarrow (x - \frac{8}{2})^{2} + 7 - (\frac{8}{2})^{2} = 0$
$\Rightarrow (x - \frac{8}{2})^{2} = - 7 + 16$
$\Rightarrow (x - 4)^{2} = 9$
$\Rightarrow (x - 4) = \pm 3$
$\Rightarrow x = 1$ or $x = 7$

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Similar questions

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

Q. Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
x² – 8x + 18 = 0

Q. Which of the following is the set of roots of the quadratic equation

x^{2} - 8 x + 7 = 0 ?

Q. are the roots of the quadratic equation

x^{2} + 6 x - 7 = 0

Q. Find the positive value of k for which quadratic equation

x^{2} - 8 x + k = 0

have real roots?

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Which of the following is/are the roots of the quadratic equation, x2−8x+7=0 ?

The correct option is D x=7Given, x2−8x+7=0 Using completing the square method we can write, x2−2(x)(82)+(82)2+7−(82)2=0 ⇒(x−82)2+7−(82)2=0 ⇒(x−82)2=−7+16 ⇒(x−4)2=9 ⇒(x−4)=±3 ⇒x=1 or x=7

Which of the following is/are the roots of the quadratic equation,
$x^{2} - 8 x + 7 = 0$ ?