If h - k and d are real and distinct numbers- then the roots of the equation x - h x - k -4 d 2 areA- real and distinct-B- imaginary-C- real and equal-D- none of these

The correct option is A real and distinct.(x+h)(x+k)=4d^2 ⇒ x^2+(h+k)x+hk 4d^2=0 D=(h+k)^2 4(hk 4d^2) =h^2+k^2+2hk 4hk+16d^2 =(h k)^2+16d^2 gt;0 ⇒ D ...

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Standard XII

Mathematics

Strictly Increasing Functions

If h , k and ...

Question

If $h, k$ and $d$ are real and distinct numbers, then the roots of the equation $(x + h) (x + k) = 4 d^{2}$ are

real and distinct.

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imaginary.

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real and equal.

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none of these

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Solution

The correct option is A real and distinct.
$(x + h) (x + k) = 4 d^{2} \Rightarrow x^{2} + (h + k) x + h k - 4 d^{2} = 0 D = (h + k)^{2} - 4 (h k - 4 d^{2}) = h^{2} + k^{2} + 2 h k - 4 h k + 16 d^{2} = (h - k)^{2} + 16 d^{2} > 0 \Rightarrow D > 0$
$∴$ roots are real and distinct

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If h,k and d are real and distinct numbers, then the roots of the equation (x+h)(x+k)=4d2 are

The correct option is A real and distinct.(x+h)(x+k)=4d2⇒x2+(h+k)x+hk−4d2=0D=(h+k)2−4(hk−4d2) =h2+k2+2hk−4hk+16d2 =(h−k)2+16d2>0⇒D>0 ∴ roots are real and distinct

If $h, k$ and $d$ are real and distinct numbers, then the roots of the equation $(x + h) (x + k) = 4 d^{2}$ are

The correct option is A real and distinct.
$(x + h) (x + k) = 4 d^{2} \Rightarrow x^{2} + (h + k) x + h k - 4 d^{2} = 0 D = (h + k)^{2} - 4 (h k - 4 d^{2}) = h^{2} + k^{2} + 2 h k - 4 h k + 16 d^{2} = (h - k)^{2} + 16 d^{2} > 0 \Rightarrow D > 0$
$∴$ roots are real and distinct