Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects

Mathematics

Nature of Roots

मूलों की प्रकृति

In Class 10 Mathematics, Nature of Roots explains how to determine the type and number of solutions of a quadratic equation. Students use the discriminant, b² − 4ac, to identify whether an equation has two distinct real roots, two equal real roots, or no real roots. The topic connects algebraic calculations with the graph of a quadratic function and helps learners interpret equations, compare cases, and solve related problems from the chapter Quadratic Equations.

Practice questions

Assertion: The equation \(x^2-10x+25=0\) has equal roots. Reason: Its discriminant is \(D=0\). Choose the correct option.MediumLevel 37A student incorrectly writes the discriminant as \(D=b^2+4ac\). What is the correct discriminant \(D\) for the quadratic equation \(x^2+2x+3=0\)?MediumLevel 37What is the nature of the roots of the equation 9x² + 12x + 4 = 0?MediumLevel 37Which option correctly describes the nature of the roots of the quadratic equation \(7x^2-2x+5=0\)?MediumLevel 37Identify the nature of roots of (2x^2-7x+3=0).MediumLevel 37What is the correct nature of the roots of \(6x^2-x-2=0\)?MediumLevel 37What is the nature of the roots of the equation \\(4x^2+4x+5=0\\)?MediumLevel 37What is the discriminant of the equation \(x^2+7x+10=0\), and what is the nature of its roots?MediumLevel 37What is the nature of the roots of the quadratic equation \(3x^2-6x+3=0\)?MediumLevel 37Which of the following quadratic equations has two real and equal roots?MediumLevel 37Which of the following equations has no real roots?MediumLevel 37If the two roots of 8x^2+px+16=09 are equal, which values of 8p9 are possible?MediumLevel 37What is the nature of the roots of the equation \(x^2-4x+1=0\)?MediumLevel 37If the discriminants of three quadratic equations are \(D_1=0\), \(D_2=7\), and \(D_3=-2\), respectively, which equation has equal roots?MediumLevel 37A situation involving a rectangle leads to the quadratic equation \(t^2-8t+16=0\). What is the nature of its roots?MediumLevel 37If the equation \\(qx^2+5x+q=0\\) has equal roots and \\(q\\ne 0\\), what are the possible values of \\(q\\)?MediumLevel 37Which condition on \(m\) is necessary for the equation \(x^2+(m-2)x+1=0\) to have no real roots?MediumLevel 37If the equation \(x^2-2(k-1)x+k+1=0\) has equal roots, what are the values of \(k\)?MediumLevel 37For the quadratic equation \(2x^2+(k-4)x+8=0\) to have no real roots, which condition on \(k\) is correct?MediumLevel 37Which statement is correct for 4x² − 4x + 1 = 0?EasyLevel 37