Question

the graph of a quadratic polynomial ax^2+bx+c=0 , having discriminant equal to zero , will touch x-axis at exactly how many points. (a)3,(b)4(c)1(d)2​

Answer 1

Answer:

(c) 1

Step-by-step explanation:

here d(discriminant) =0,so it have real and equal roots.

Answer 2

Option C (1) is the correct answer.

• It is given that a quadratic polynomial$ax^2 +bx+c=0$ has its discriminant value as 0.

• Consider the quadratic expression$ax^2 +bx+c=0$,

=> Discriminant of a quadratic equation of the above form is given by the formula, D = $\sqrt[2]{b^2-4ac}$ where a,b are the coefficients of x^2 and x respectively.

• The nature of the quadratic equation graph can be decided by the discriminant value, If D>0 then the roots are distinct and also has real values, it intersects the x-axis at two points.
• if D=0, only one unique solution is possible in this case and the solution is real, the graph touches the x-axis only at one point.
• If D<0 the solutions are imaginary and the graph will not intersect with the x-axis at any points.

• As the given polynomial has a discriminant value equal to 0, hence the roots are equal and the equation touches the x-axis only at one point.

Therefore, Option C is the correct answer.