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5 days ago · So here we can see that roots are unequal and imaginary. We cannot solve it by completing the square method. Note: Read the question carefully. Be thorough with the concepts. You should know the nature of roots i.e. when the roots are real, imaginary etc. Also, while finding roots do not miss any term. Also, don’t miss any sign.
3 days ago · Given two roots of the biquadratic equation are \[1+i\], \[1-\sqrt{2}\]. We can find the other two roots of the biquadratic equation by using the conjugates of the given roots. To find the conjugate of complex numbers, we have to change the sign of the imaginary part. So, we will get the conjugate of \[1+i=1-i\].
3 days ago · Note: While solving this question we used the formula where the relation between the two roots $\alpha$ and $\beta$ are there, because option is given like the relation between the $\alpha$ and $\beta$, so that is why we use that relation formula. but you can also use the quadratic formula but this will lead to a clumsy and lengthy solution.
4 days ago · We are also given that $\alpha -\beta =11$ . We have to solve these two equations and find the value of $\alpha $ and $\beta $ . For a quadratic polynomial, the product of the roots is equal to $\dfrac{c}{a}$ . We have to compare the standard form to the given polynomial, substitute the values in the equation and solve for k.
3 days ago · One root is the square of the other root, \[b = {a^2}\]. Now let’s get the relation between the coefficients of the quadratic equation. 1 The sum of the roots of the quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient. \[ \Rightarrow [a(a + 1)] = - p\] 2.The product of the ...
1 day ago · Hint: Every quadratic equation is of the form \[a{x^2} + bx + c = 0\], here, \[a,b,c\] are real and rational numbers. We are going to find the roots of the equation or assume the roots of the equation. From that, we will solve the equation. Formula used: Sum of the roots:
3 days ago · The constant term of the equation will give the product of the two roots of the equation \[\dfrac{c}{a}\] . Now, using these properties, one could get to the solution. Complete step by step answer: Every quadratic equation is in the form, ${{x}^{2}}-Sx+P=0$(where ‘S’ is the sum of the roots and ‘P’ is the product the roots).
