Solution of Quadratic and Higher Degree Equations
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Complex Numbers and Quadratic Equation

118165 If both the roots of the quadratic equation \(x^2-\) \(2 k x+k^2+\mathbf{k}-5=0\) are less than 5 , then \(k\) lies in the interval

1 \([4,5]\)
2 \((-\infty, 4)\)
3 \((6, \infty)\)
4 \((5,6]\)
Complex Numbers and Quadratic Equation

118166 Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots \((4,3)\). Rahul made a mistake in writing down coefficient of \(x\) to get roots \((3,2)\). The correct roots of equation are

1 \(-4,-3\)
2 6,1
3 4,3
4 \(-6,-1\)
Complex Numbers and Quadratic Equation

118167 The equation \(e^{\sin x}-e^{-\sin x}-4=0\) has

1 infinite number of real roots
2 no real root
3 exactly one real root
4 exactly four real roots
Complex Numbers and Quadratic Equation

118168 If \(a \in R\) and the equation \(-3(x-[x])^2+2(x-\) \([x])+a^2=0\) (where, \([x]\) denotes the greatest integer \(\leq x\) ) has no integral solution, then all possible values of a lie in the interval

1 \((-1,0) \cup(0,1)\)
2 \((1,2)\)
3 \((-2,-1)\)
4 \((-\infty,-2) \cup(2, \infty)\)
Complex Numbers and Quadratic Equation

118165 If both the roots of the quadratic equation \(x^2-\) \(2 k x+k^2+\mathbf{k}-5=0\) are less than 5 , then \(k\) lies in the interval

1 \([4,5]\)
2 \((-\infty, 4)\)
3 \((6, \infty)\)
4 \((5,6]\)
Complex Numbers and Quadratic Equation

118166 Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots \((4,3)\). Rahul made a mistake in writing down coefficient of \(x\) to get roots \((3,2)\). The correct roots of equation are

1 \(-4,-3\)
2 6,1
3 4,3
4 \(-6,-1\)
Complex Numbers and Quadratic Equation

118167 The equation \(e^{\sin x}-e^{-\sin x}-4=0\) has

1 infinite number of real roots
2 no real root
3 exactly one real root
4 exactly four real roots
Complex Numbers and Quadratic Equation

118168 If \(a \in R\) and the equation \(-3(x-[x])^2+2(x-\) \([x])+a^2=0\) (where, \([x]\) denotes the greatest integer \(\leq x\) ) has no integral solution, then all possible values of a lie in the interval

1 \((-1,0) \cup(0,1)\)
2 \((1,2)\)
3 \((-2,-1)\)
4 \((-\infty,-2) \cup(2, \infty)\)
Complex Numbers and Quadratic Equation

118165 If both the roots of the quadratic equation \(x^2-\) \(2 k x+k^2+\mathbf{k}-5=0\) are less than 5 , then \(k\) lies in the interval

1 \([4,5]\)
2 \((-\infty, 4)\)
3 \((6, \infty)\)
4 \((5,6]\)
Complex Numbers and Quadratic Equation

118166 Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots \((4,3)\). Rahul made a mistake in writing down coefficient of \(x\) to get roots \((3,2)\). The correct roots of equation are

1 \(-4,-3\)
2 6,1
3 4,3
4 \(-6,-1\)
Complex Numbers and Quadratic Equation

118167 The equation \(e^{\sin x}-e^{-\sin x}-4=0\) has

1 infinite number of real roots
2 no real root
3 exactly one real root
4 exactly four real roots
Complex Numbers and Quadratic Equation

118168 If \(a \in R\) and the equation \(-3(x-[x])^2+2(x-\) \([x])+a^2=0\) (where, \([x]\) denotes the greatest integer \(\leq x\) ) has no integral solution, then all possible values of a lie in the interval

1 \((-1,0) \cup(0,1)\)
2 \((1,2)\)
3 \((-2,-1)\)
4 \((-\infty,-2) \cup(2, \infty)\)
Complex Numbers and Quadratic Equation

118165 If both the roots of the quadratic equation \(x^2-\) \(2 k x+k^2+\mathbf{k}-5=0\) are less than 5 , then \(k\) lies in the interval

1 \([4,5]\)
2 \((-\infty, 4)\)
3 \((6, \infty)\)
4 \((5,6]\)
Complex Numbers and Quadratic Equation

118166 Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots \((4,3)\). Rahul made a mistake in writing down coefficient of \(x\) to get roots \((3,2)\). The correct roots of equation are

1 \(-4,-3\)
2 6,1
3 4,3
4 \(-6,-1\)
Complex Numbers and Quadratic Equation

118167 The equation \(e^{\sin x}-e^{-\sin x}-4=0\) has

1 infinite number of real roots
2 no real root
3 exactly one real root
4 exactly four real roots
Complex Numbers and Quadratic Equation

118168 If \(a \in R\) and the equation \(-3(x-[x])^2+2(x-\) \([x])+a^2=0\) (where, \([x]\) denotes the greatest integer \(\leq x\) ) has no integral solution, then all possible values of a lie in the interval

1 \((-1,0) \cup(0,1)\)
2 \((1,2)\)
3 \((-2,-1)\)
4 \((-\infty,-2) \cup(2, \infty)\)