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Given below are two statements, followed by four conclusions. Assume the facts in the statements to be true and decide which of the conclusions logically follow(s) from the statements. Statements: All roots are fruits. All fruits are guns. Conclusions: I. All roots are guns,. II. All guns are roots. III. All fruits are roots. IV. Some guns are roots.
Given two quadratic equations, I. x2 - 31x + 240 = 0 Equation I has two roots x1, x2. (x1 > x2) II. 3y2 – 7y – 3 = 8y - 3y2 - 9 Equation II has two roots y1, y2. (y2 > y1) Find the equation whose roots are (– 2y1 + x1), - (y2 – x2).
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements. Statements: All woods are roots. All fruits are roots. No woods are a fruit. Conclusion: (I) Some roots are fruits. (II) All roots are woods.
Consider the statements given below: A: Sum of roots of a quadratic equation ax2 + bx + c = 0 is (c/a). B: If one root of a quadratic equation is (p + qi), then root must be (q + pi). C: Roots of the equation 3x2 + 4x = 5 are all real. Which of the statement(s) is/are TRUE?
Consider the following statements in respect of the roots of the equation x3 - 8 = 0: 1. The roots are non-collinear. 2. The roots lie on a circle of unit radius. Which of the above statements is/are correct?
In the quadratic equation ax2 - bx + c = 0, if the given equation has equal roots and the product of both roots is 4, then, what is the ratio of b : c?
The characteristic equation of a control system is s(s2+ 6s+13)+K=0. The value of k such that the characteristic equation has a pair of complex roots with real part -1 will be :
If the characteristic equation of the differential equation $$\frac{{{{\text{d}}^2}{\text{y}}}}{{{\text{d}}{{\text{x}}^2}}} + 2\alpha \frac{{{\text{dy}}}}{{{\text{dx}}}} + {\text{y}} = 0$$     has two equal roots, then the values of $$\alpha $$ are
A class III mathematics teacher gave the following questions to her students:  \(\begin{equation} \frac{ \begin{array}[b]{r} 256 \\ + 173 \end{array} }{ } \end{equation}\) \(\begin{equation} \frac{ \begin{array}[b]{r} 28 \\ + 32 \end{array} }{ } \end{equation}\) \(\begin{equation} \frac{ \begin{array}[b]{r} 129 \\ + 76 \end{array} }{ } \end{equation}\) Later she asks the students to solve a worksheet that has similar questions. Which of the following statements is appropriate for the given situation?
Which of the following is true? A: If the sum of cube of three numbers is thrice the product of the three numbers, then the sum of three numbers will be non-zero. B: For quadratic equation ax2 + bx + c = 0, If b2 < 4ac, then the given equation has only one real root. C: In the equation, x2 – (a + b)x + ab = 0, the roots of this equation will be ‘a’, ‘b’.