Mathematics
Roots of a Quadratic Equation
द्विघात समीकरण के मूल
Roots of a Quadratic Equation, taught in Class 10 Mathematics under the chapter Quadratic Equations, introduces the values of the variable that make a quadratic expression equal to zero. Students learn to identify roots, verify them by substitution, and connect the sum and product of the roots with the coefficients. The topic also helps them form a quadratic equation when its roots are known and use these relationships to solve and check mathematical problems.
Practice questions
If (x-4) and (x+7) are factors of a quadratic equation, what are its roots?MediumLevel 32The two roots of the equation \(x^2+px+25=0\) are \(-5\) and \(-5\). What is the value of \(p\)?MediumLevel 32If (x=\frac{4}{3}) is a root of (3x^2-7x+c=0), what is the value of (c)?MediumLevel 32If \(a=1\), \(b=-16\), and \(c=64\) in a quadratic equation, what are its roots?MediumLevel 32If the product of roots of a quadratic equation is negative, which statement is correct?MediumLevel 32What are the roots of (x^2+x-20=0)\)?MediumLevel 32If \(\alpha\) and \(\beta\) are the roots of the equation \(x^2-8x+15=0\), what is the value of \(\alpha+\beta+\alpha\beta\)?MediumLevel 32Which expression's sign is used to determine the nature of the roots of a quadratic equation?MediumLevel 32What is the repeated root of the equation \(16x^2-8x+1=0\)?MediumLevel 32If (x=0) is a root of the equation (ax^2+bx+c=0), where (a\ne0), which of the following conclusions is correct?MediumLevel 32If \(x=2\) and \(x=7\) are the roots of a monic quadratic equation, what is the coefficient of \(x\)?MediumLevel 32What are the roots of the equation \(3x^2+2x-8=0\)?MediumLevel 32If the roots of the equation \\(x^2+mx+20=0\\) are \\(-4\\) and \\(-5\\), what is the value of \\(m\\)?MediumLevel 32If the roots of a quadratic equation are 5 and 1/5, which statement is correct about them?EasyLevel 32What is the positive root of the equation \(x^2-5x-24=0\)?MediumLevel 32If the discriminant \(D=0\) and the sum of the roots is \(12\), what is the value of each root?MediumLevel 32What is the absolute difference between the roots of \(x^2-6x-7=0\)?MediumLevel 32If \(\alpha\) and \(\beta\) are the roots of the equation \(3x^2-12x+5=0\), what is the value of \(\alpha+\beta\)?MediumLevel 32What is the condition for the quadratic equation \(ax^2+bx+c=0\), where \(a\ne0\), to have two equal real roots?MediumLevel 32For the quadratic equation \(x^2+4x+k=0\) to have real roots, which condition on \(k\) is necessary?MediumLevel 32