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

Polynomials in one variable

एक चर वाले बहुपद

In this Class 10 Mathematics topic from the chapter “Polynomials,” students study algebraic expressions involving a single variable, such as x. They learn to identify a polynomial and its degree, understand constant, linear, quadratic, and cubic forms, and find its zeroes or roots. The topic also develops understanding of the relationship between zeroes and coefficients, helping students interpret polynomial equations and solve related problems accurately.

Practice questions

If a polynomial in one variable has degree 4, which statement about its number of real zeroes is definitely true?ExpertLevel 46For p(x)=x^2-2x+2, what is the correct conclusion about its real zeroes?MediumLevel 46If (p(x)=x^2-7x+10) and (q(x)=p(x+1)), what are the zeroes of (q(x))?ExpertLevel 46If (p(x)=x^3+ax^2+bx-12), (p(2)=0), and (p(3)=0), what is the value of (a+b)?HardLevel 48If p(x) = x^4 + mx^2 + 16 can be written as (x^2 - 4)^2, what is m?MediumLevel 48If p(x) = 2x^2 - 5x + 3, what is p(x + 2) - p(x)?MediumLevel 48If the degree of (p(x)=(a-1)x^6+(a+2)x^4-5x+7) is (4), what will (a) be?ExpertLevel 47If (p(x)=kx^3+2x^2-7x+5) and (p(-1)=16), what is the value of (k)?ExpertLevel 47What is the coefficient of x³ in the sum of p(x) = 5x⁴ − 3x³ + 2x² − x + 8 and q(x) = −2x⁴ + 7x³ − 5x² + 4x − 6?MediumLevel 47What is the degree of the sum of (p(x)=6x^5-4x^2+1) and (q(x)=-6x^5+3x^4+x-9)?ExpertLevel 47If non-zero polynomial (p(x)) has degree (6) and (q(x)) has degree (3), what will be the degree of (p(x)q(x))?ExpertLevel 47What is the coefficient of (x^2) in ((3x-2)(2x^2+x-5))?ExpertLevel 47If x = -3 is a zero of p(x) = x^2 + kx - 18, what is k?MediumLevel 48For the polynomial \(p(x)=4x^3-11x^2+6x+2\), what is the value of \(p(2)\)?ExpertLevel 47Which of the following expressions is a polynomial in one variable \(x\) with real coefficients?ExpertLevel 47For the polynomial \(p(x)=x^4-10x^2+9\), what is the value of \(p(-3)\)?ExpertLevel 47If p(x)=x²+ax+b satisfies p(-2)=0 and p(5)=0, what is the value of a+b?ExpertLevel 47If the zeros of the polynomial \(p(x)=x^2+ax+b\) are \(-4\) and \(1\), what is the value of \(b\)?ExpertLevel 47Which expression is not a polynomial because the variable has a fractional power?ExpertLevel 47If a = 0, b ≠ 0, and c ≠ 0 in p(x) = ax⁵ + bx⁴ + cx³ + d, what will be the degree of p(x)?MediumLevel 47