Nature of Roots
Find the values of p if the equation x2−x+p=0 does not possess real roots.
(A) p > 18
(B) p > 14
(C) p > 12
(D) p > 1
The condition for the equation x2+bx+c=0 to have real roots is ____.
Vijay inherited a large amount of wealth from his father and by establishing a soft drinks company, he squared his wealth. He then started a company which manufactured airplane toys and incurred huge losses amounting to k (>0) times the wealth he inherited from his father. His total assets now stand at a debt of 4 crore. Comment on the value of k.
Any value of “k” is possible
k is any value greater than or equal to 4
None of the above
Depends on what amount is inherited initially - “x”
Comment on the nature of the roots of the equation 2x2–6x+8=0
real, unequal and rational
real and equal
real, unequal and irrational
Find the value of k for which the quadratic equation x2–4x+k=0 has real and equal roots.
The equation x2+x−5=0 has two distinct real roots.
Solve for x if 4(2x+3)2−(2x+3)−14=0.
In the figure given above, PA and PB are tangents to the circle from point P. How many real values of x exist such that the length of PA is x and length of PB is x2+1?
The number of real roots of the equation x2−3x+5=0 is:
A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and takes two hours longer to cover the distance. Assuming the uniform speed to be 'x' km/h, form an equation and solve it to evaluate 'x'.