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प्रश्न
If one root of the equation 2x² – px + 4 = 0 is 2, find the other root. Also find the value of p.
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उत्तर
The given quadratic equation is
2x² – px + 4 = 0
one root = 2
Let the other root be a
The sum of the roots 2 + a = `(-(-p))/(2) = p/(2)`
a = `p/(2) - 2` ...(i)
The product of the roots
a x 2 = `(4)/(2) = 2`
⇒ a = 1
Now 2 + a = `p/(2)`
⇒ 2 + 1 = `p/(2)`
⇒ p = 6.
संबंधित प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
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For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
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In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
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