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1. www.vedantu.com › question-answer › if-the-roots-ofIf the roots of the quadratic equations \\[h{x^2} + 21x + 10 ...

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   3 days ago · So let us assume that the roots of the ratios are $2x$ and $5x$ Then, the sum of roots will be equals to $2x + 5x = 7x$ And the product of the roots will be $2x \times 5x = 10{x^2}$ As we've got found within the formula, For the condition \[h{x^2} + 21x + 10 = 0\] At that point, the sum of zeroes $ = \dfrac{{ - 21}}{h}$

2. www.vedantu.com › question-answer › hm-between-theHM between the roots of the equation \[{x^2} - 10x - Vedantu

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   3 days ago · First, we will find the roots of the given equation since the given equation is a quadratic equation it will have two roots. Then we will find the harmonic equation of those roots using the formula. Formula Used: If \[\alpha \]and \[\beta \] are the roots then the quadratic equation can be written as\[{x^2} - (\alpha + \beta )x + \alpha \beta ...

3. www.vedantu.com › question-answer › if-the-roots-ofIf the roots of the equation $ { {x}^ {2}}+ax+b=0$ are $c ...

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   5 days ago · Hint: To solve this question we need to have knowledge about solving quadratic equations. To solve this question we need to represent the quadratic equation as the product and sum of the roots, where roots are the number which actually make the quadratic equation result to zero. Complete step by step answer:

4. www.vedantu.com › question-answer › the-biquadraticThe biquadratic equation, two of whose roots are \\[1+i ...

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   3 days ago · Be clear about forming the quadratic equation with the given roots and also a biquadratic equation is formed by the product of two quadratic equations. There is a possibility that some students might try to substitute the roots in the given options and check if it satisfies or not.

5. www.vedantu.com › question-answer › if-the-roots-ofIf the roots of the equation $a { {x}^ {2}}+bx+c=0$ are real ...

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   4 days ago · Hint: We start solving the problem by using the fact that discriminant should be greater than zero for roots to become real and distinct. We now assume a positive number for discriminant and substitute this in the roots of the quadratic equation.

6. www.vedantu.com › question-answer › if-one-root-ofIf one root of the quadratic equation $ 2{x^2} + kx - 6 = 0 ...

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   3 days ago · The values of $ x $ satisfying the quadratic equation are known as the roots of the quadratic equation. We can find the value of other roots by using the sum and the product formula of the roots. Complete step by step solution: As per the given question we have an equation $ 2{x^2} + kx - 6 = 0 $ and one of the roots is $ 2 $ . We will find the ...

7. www.vedantu.com › question-answer › if-one-root-isIf one root is the square of the other root of the equation

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   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 ...