To calculate: The discriminant of the equation k(x)=25x2−10x+1 and the number of x-intercepts for the function.

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broliY · Accepted Answer

Step 1 For a quadratic equation of the form ax2+bx+c=0(a≠0) the discriminant is b2−4ac. Furthermore: If b2−4ac&amp;gt;0 and not a perfect square then there will be two irrational solutions. If b2−4ac&amp;gt;0 and a perfect square then there will be two rational solutions. If b2−4ac&amp;lt;0 then there will be two imaginary solutions. If b2−4ac=0 then there will be one rational solution. Step 2 Consider the provided function: k(x)=25x2−10x+1 Now, as it can be observed thet the function contains a quation and for a quadratic equation of the form ax2+bx+c=0(a≠0) the discriminant is b2−4ac Now, for the provided quadratic equation, a=25, b=−10 and c=1 Thus, substitute 25 for a, -10 for b and 1 for c in the formula of discriminant as: b2−4ac=(−10)2−4(25)(1) =100−100 =0 Thus, the required discriminant is 0. Furthermore: If b2−4ac&amp;gt;0 and not a perfect square then there will be two irrational solutions. If b2−4ac&amp;gt;0 and a perfect square then there will be two rational solutions. If b2−4ac&amp;lt;0 then there will be two imaginary solutions. If b2−4ac=0 then there will be one rational solution. Now, since for the provided equation:

To calculate: The discriminant of the equation k(x)=25x^{2}-10x+1 and the

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