If the roots of ax^(2)+x+b=0 be real and...

If the roots of `ax^(2)+x+b=0` be real and unequal, show that the roots of `(x^(2)+1)/(x)=4sqrt(ab)` are imaginary.

Topper's Solved these Questions

QUADRATIC EQUATIONS
ICSE|Exercise EXERCISE 10 (d)|14 Videos
QUADRATIC EQUATIONS
ICSE|Exercise EXERCISE 10 (e)|4 Videos
QUADRATIC EQUATIONS
ICSE|Exercise EXERCISE 10 (b)|16 Videos
PROPERTIES OF TRIANGLE
ICSE|Exercise EXERCISE 7|38 Videos
RELATION AND FUNCTIONS
ICSE|Exercise MULTIPLE CHOICE QUESTIONS (Choose the correct answer from the given four options in questions)|32 Videos

Similar Questions

Explore conceptually related problems

If the roots of the equation qx^(2)+2px+2q=0 are real and unequal, prove that the roots of the equation (p+q)x^(2)+2qx+(p-q)=0 are imaginary.

If roots of equation x^2-2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

If roots of equation x^3-2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

If the roots of the equation x^2+2c x+a b=0 are real and unequal, then the roots of the equation x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: (a) real and unequal (b) real and equal (c) imaginary (d) rational

If the roots of the equation , x^2+2c x+ab=0 are real and unequal, then the roots of the equation, x^2-2(a+b)x+(a^2+b^2+2c^2)=0 are: a. real and unequal b. real and equal c. imaginary d. Rational

If the roots of ax^2+2bx+c=0 be possible and different then show that the roots of (a+c)(ax^2+2bx+2c)=2(ac-b^2)(x^2+1) will be impossible and vice versa

The equation ax^(4)-2x^(2)-(a-1)=0 will have real and unequal roots if

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.

The roots of the equation x^2+ax+b=0 are

Show that A.M. of the roots of x^(2) - 2ax + b^(2) = 0 is equal to the G.M. of the roots of the equation x^(2) - 2b x + a^(2) = 0 and vice- versa.

ICSE-QUADRATIC EQUATIONS-EXERCISE 10 (c)

If the equation (1+m^(2))x^(2)+2mcx+c^(2)-a^(2)=0 has equal roots, sho...
Text Solution
|
Find the value of m so that the roots of the equation (4-m)x^(2)+(2m+4...
Text Solution
|
If the roots of ax^(2)+x+b=0 be real and unequal, show that the roots ...
Text Solution
|
Find 'a' so that the sum of the roots of the equation ax^(2)+2x-3a=0 m...
Text Solution
|
If alpha,beta are the roots of the equation x^(2)+x+1=0, find the valu...
Text Solution
|
If alpha,beta are the roots of the equation x^(2)+px+q=0, find the val...
Text Solution
|
If the roots of the equation x^(2)+px+7=0 are denoted by alpha and bet...
Text Solution
|
If alpha,beta are the roots of the equation 3x^(2)-6x+4=0, find the va...
Text Solution
|
If alpha,beta are the roots of ax^(2)+bx+c=0, find the value of (i) ...
Text Solution
|
If the sum of the roots of the equation x^(2)-px+q=0 be m times their ...
Text Solution
|
If one root of the equation x^(2)+ax+8=0 is 4 while the equation x^(2)...
Text Solution
|
Find the value of a for which one root of the quadratic equation (a^(2...
Text Solution
|
If alpha,beta are the roots of the equation ax^(2)-bx+b=0, prove that ...
Text Solution
|
If alpha and beta are the roots of the equation x^(2)+x-7=0, form the ...
Text Solution
|
If alpha and beta are the roots of the equation 2x^(2)+3x+2=0, find th...
Text Solution
|
Find the equation whose roots are (alpha)/(beta) and (beta)/(alpha), w...
Text Solution
|
If alpha and beta are the roots of the equation 2x^(2)-3x+1=0, form th...
Text Solution
|
If a ne b and a^(2)=5a-3,b^(2)=5b-3, then form that equation whose roo...
Text Solution
|
Given that alpha and beta are the roots of the equation x^(2)=x+7. (...
Text Solution
|
Given that alpha and beta are the roots of the equation x^(2)-x+7=0, f...
Text Solution
|