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If the difference of roots of the equation \( \Large x^{2}-bx+c=0 \) be 1, then;

A) \( \Large b^{2}-4c-1=0 \)
B) \( \Large b^{2}-4c=0 \)
C) \( \Large b^{2}-4c+1=0 \)
D) \( \Large b^{2}+4c-1=0 \)

Correct Answer:

A) \( \Large b^{2}-4c-1=0 \)

Description for Correct answer:
Let \( \Large \alpha \) and \( \Large \beta \) are the roots of equation \( \Large x^{2}-bx+c=0 \)

=> \( \Large \alpha + \beta = b\ and\ \alpha \beta = c\)

=> \( \Large \alpha + \beta = \sqrt{ \left( \alpha + \beta \right)^{2}-4 \alpha \beta } \)

=> \( \Large 1 = \sqrt{b^{2}- 4c} \)

=> \( \Large b^{2}-4c-1=0 \)

Part of solved Quadratic Equations questions and answers : >> Elementary Mathematics >> Quadratic Equations

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Similar Questions

1). If \( \Large 2+i\sqrt{3} \) is a root of the equation \( \Large x^{2}+px+q=0 \) where p and q are real, then \( \Large p, q \) is equal to:

A). (-4, 7)

B). (4,-7)

C). (4, 7)

D). (-4, -7)

2). If \( \Large x=\sqrt{1+\sqrt{1+\sqrt{1}+.....}} \), the x is equal to

A). \( \Large \frac{1+\sqrt{5}}{2} \)

B). \( \Large \frac{1-\sqrt{5}}{2} \)

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3). If \( \Large \alpha , \beta \) are the roots of equation \( \Large ax^{2}+bx+c=0 \), then \( \Large \frac{ \alpha }{ \alpha \beta +b}+\frac{ \beta }{ \alpha x+b} \) is equal to

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4). If the roots of the equation \( \Large \frac{ \alpha }{x- \alpha }+\frac{ \beta }{x- \beta }=1 \) be equal in magnitude but opposite in sign, then \( \Large \alpha + \beta \) is equal to:

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5). If the roots of the equation \( \Large px^{2}+2qx+r=0 \) and \( \Large qx^{2}-2\sqrt{pr}x+q=0 \) be real, then:

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B). \( \Large q^{2}=pr \)

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6). If one root of the quadratic equation \( \Large ax^{2}+bx+c=0 \) is equal to nth power of the other root, then the value of \( \Large \left(ac^{n}\right)^{\frac{1}{n+1}} + \left(a^{n}c\right)^{\frac{1}{n+1}} \) is equal to

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7). The quadratic in t, such that AM of its roots is A and GM is G is:

A). \( \Large t^{2}-2At+G^{2}=0 \)

B). \( \Large t^{2}-2At-G^{2}=0 \)

C). \( \Large t^{2}+2At+G^{2}=0 \)

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8). If \( \Large n^{2}px+1 \) is a factor of expression \( \Large ax^{3}+bx+c \) then:

A). \( \Large a^{2}+c^{2}=-ab \)

B). \( \Large a^{2}-c^{2}=-ab \)

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B). \( \Large 1+\sqrt{2} \)

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