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This is because it contains a minus sign which can only result from product of two quantities having opposite signs. Another way to prevent getting this page in the future is to use Privacy Pass. $$x$$ = $$\frac{-b + √{D}}{2a} ~or~\frac{-b -√{D}}{2a}$$, $$x$$ = $$-\frac{b}{2a}~ or~-\frac{b}{2a}$$. Since D<0, the equation will have two distinct Complex roots. Let us analyze all the possibilities and see how it affects the roots of the equation. This means the graph of the equation will not intersect. Your IP: 185.86.150.76 The value of x for which a quadratic equation agrees is known as roots of the quadratic equation. Understand the concept of discriminant to classify roots of quadratic equation as real and distinct and also as real and equal. Let us take some examples for better understanding. ax 2 + bx + c = 0 (Here a, b and c are real and rational numbers) To know the nature of the roots of a quadratic-equation, we will be using the discriminant b 2 - 4ac. If we have $$√{-225}$$, we can never write it as a product of two equal quantities. The quadratic equation whose roots are real and equal is: x 2 – 4x + 4 = 0 2x 2 – 4x + 3 = 0 x 2 – 2 √2 – 6 = 0 A polynomial equation whose degree is 2, is known as quadratic equation. Also, take free tests to practice for exams. This quantity is called discriminant of the quadratic equation. 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Your email address will not be published. Revise Mathematics chapters using videos at TopperLearning ... CBSE Class 10 Maths Nature of Roots. Performance & security by Cloudflare, Please complete the security check to access. To solve more problems on the topic, download BYJU’S – The Learning App from Google Play Store and watch interactive videos. Question 13 of 30. Let us put this to practice. A quadratic equation in its standard form is represented as: $$ax^2 + bx + c$$ = $$0$$, where $$a,~b ~and~ c$$ are real numbers such that $$a ≠ 0$$ and $$x$$ is a variable. D = Since D > 0, the equation will have two real roots and distinct roots. Question 13 of 30. We already know what a quadratic equation is, let us now focus on nature of roots of quadratic equation. The nature of the roots of following quadratic equation Unequal Equal No real roots None of above. So, a quadratic equation has two roots. Roots of the Quadratic Equation. Q. Before going ahead, there is a terminology that must be understood. Is $$√{-k}$$ a real number? This means the graph of the equation will intersect, D = 0: When D is equal to zero, the equation will have two real and equal roots. 14. Find the value of k for which the roots of this equation are real and equal k^2 x^2 - 2(2k-1)x + 4= 0 Prove that both the roots of the equation (x-a)(x-b)=m^2 are always real. In terms of D, the roots can be written as: $$x$$ = $$\frac{-b ± √{D}}{2a}$$ ——————————— (1). The roots are: $$x$$ = $$\frac{-b + √D}{2a}$$ or $$\frac{-b – √D}{2a}$$, $$x$$ = $$\frac{-5 + √1}{2 × 1}$$ or $$\frac{-5 – √1}{2~×~1}$$, D = $$1^2 – 4~×~1~×~1$$ = $$1~ -~ 4$$ = $$-3$$. A quadratic equation can have two different roots, two similar roots or real roots … The answer is no. Cloudflare Ray ID: 5fa14f0fb89b1665 Solution: Here the coefficients are all rational. if we have $$√225$$, we can write it as $$√({15~×~15})$$ which is equal to $$15$$. 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