Graph of polynomial `x^2-5x+4`will intersect x axis exactly at two distinct points. True or False

Polynomial ax^2+c has two zeroes which are equal in magnitude but opposite in sign. True or False

The equation ax^2+2x+a=0 has two distinct roots,if

The graph of a linear polynomial cross the x-axis

If the zeroes of the polynomial x^2-5x+k are the reciprocal of each other, then find the value of k.

Find the zeroes of the polynomial p(x)=x^3-5x^2-2x+24 if it is given that the product of the two zeroes is 12.

If 4+sqrt5 is a zero of polynomial. x^3+bx^2-5x+c then find the b and c where b and c are rational numbers.

Two lines parallel to the y-axis and at a distance of2 units from the x-axis are taken. Another two lines parallel to the x-axis and at a distance of 3 units from the y-axis are also taken. Find the distance of the angular points of the rectangle, formed by the four intersecting line segments, from the origin.

Fill in the blank: The ______ of a polynomial are the x-coordinates of the point of intersection i.e. where y coordinate is ________.

Find the zeroes of the quadratic polynomial p(x)=2x^2+5x-12 and verify the relationship between the zeroes and its coefficients.

If alpha and beta are the two zeroes of the quadratic polynomial x^2-3x+7 , find a quadratic polynomial whose zeroes are 1/alpha and 1/beta .